Search

The first direct detection of gravitational waves (GWs) from a black-hole (BH) binary, GW150914, by the advanced Laser Interferometer Gravitational-wave Observatory (aLIGO) detectors in 2015 heralded a new era in GW physics. Since then, over 90 compact binary merger events have been detected by the GW detector network with many more expected in the decades to come. A significant part of the theoretical foundations that underpins this achievement is the modelling of GW sources in General Relativity (GR) using numerical relativity (NR). In this thesis, we discuss the features and capabilities of the NR code GRChombo. Although GRChombo is no longer a new code, its original development and design targeted applications beyond the conventional astrophysical paradigm that other NR codes have focussed on. Here, we describe more recent additions that have allowed GRChombo to model BH binaries and other GW sources with good accuracy. Through direct comparison, we demonstrate that this accuracy is comparable to that of a more mature NR code. One of the key capabilities of GRChombo is its adaptive mesh refinement (AMR). This allows the numerical grid to dynamically adjust itself in order to sufficiently resolve the large range of spatial and temporal scales that characteristically arise in non-trivial solutions of GR as a consequence of the theory's non-linearity. However, this flexibility requires careful control in order to achieve the desired accuracy and we discuss in detail the lessons learned in order to achieve this with GRChombo. We apply GRChombo and these techniques to the investigation of the effect of orbital eccentricity on the GW emission and the gravitational recoil imparted to the BH merger remnant from the inspiral and merger of unequal-mass non-spinning BH binaries. Finally, we explore the modelling of a more exotic type of compact object: boson stars (BSs) which are comprised of complex scalar field matter. In particular, we investigate the construction of suitable initial data describing BS binaries and its effect on the ensuing evolutions.

Weak bosons are by now a well-established and observed block of the elementary particles table, but the era of Precision Physics opens up new ways of utilising them in an attempt to uncover the mystery of physics beyond the Standard Model. Being central to what is called Electroweak Symmetry Breaking mechanism, they obtain mass by interacting with the Higgs field. Their longitudinal polarisation is induced by the Goldstone modes of the Higgs field and provides a direct handle on any massive new physics models. In this thesis, we devote a particular focus on the polarised W-boson production in the context of two processes at the LHC and explore applications of our results. We discuss in depth the current approaches to simulate and measure weak boson polarisation, and present NNLO studies of W+j and W+ W− production at the LHC. We explore the effects and significance of observed perturbative corrections, and in the context of W+j, comment on their application to experimental data. In addition to that, we discuss how polarisation quantities, in particular, angular coefficients, are instrumental in precise W-boson mass measurements which aim to reach 0.01% level of precision. Aiming to fill the gap for precise theoretical input, we provide NNLO + NLO EW predictions, and comment on their effects and theoretical uncertainty. Furthermore, we explore advancements in the area of fixed-order predictions in general and present results for Wbb̄ production at NNLO precision. This is the first study of a 2 → 3 process involving a massive particle at such accuracy, which marks a milestone following significant advancements in the field. We also discuss the novel proposition for a flavoured anti-kT algorithm, which aims to combine the experimental convenience of anti-kT prescription with a modification for flavoured particles, enabling IR-safe heavy flavour tagging with two real emissions. Results based on this prescription are compared with the well-established flavour-kT method and to available data. Lastly, we introduce the new framework named HighTEA, which as we hope, will be helpful for the researchers who use the output of fixed order predictions. We present the ideas and structure of the project, the details of its current capabilities, its limitations and aspirations, and provide with user instructions to quickly bring an interested reader up to speed.

In this thesis we study string compactifications on manifolds equipped with a G-structure, placing a special emphasis on the interplay between geometry and physics. We follow two complementary approaches. In the first part of the thesis we adopt a sigma model perspective and focus on the worldsheet superconformal field theory. We consider compactifications on 7-dimensional Extra Twisted Connected Sum (ETCS) G2 manifolds as well as 8-dimensional Generalized Connected Sum (GCS) Spin(7) manifolds. These are special holonomy manifolds obtained by gluing together two open manifolds along isomorphic asymptotic ends in a particular fashion. We find that this geometric construction is reproduced in the worldsheet algebra via a diamond of algebra inclusions. A study of the automorphisms of these algebras leads us to conjecture new mirror maps for GCS manifolds. Finally, we explore-making use of the worldsheet algebras-whether these constructions produce manifolds of generic special holonomy. In the second part of the thesis we change gears and consider string compactifications from a supergravity point of view. In particular, we focus on compactifications of the heterotic string down to three spacetime dimensions preserving minimal supersymmetry N = 1. These are described by the heterotic G2 system, which is the 7-dimensional analogue of the Hull-Strominger system. Finding solutions to this system involves the study of 7-dimensional manifolds with integrable G2-structures and the construction of G2-instantons on bundles over them. In addition, the anomaly cancellation condition mixes the different degrees of freedom of the theory in a highly non-trivial way. As a result, explicit background solutions are difficult to obtain. We construct new families of solutions to the system on homogeneous 3-Sasakian manifolds-that means either the 7-sphere or the Aloff-Wallach space N(1,1)-equipped with squashed metrics. Our solutions present constant dilaton and AdS3 spacetime. Some of these families can be regarded as finite deformations from a given solution, providing an explicit description of a particular direction in the moduli space.

Directional amplification, in which signals are selectively amplified depending on their propagation direction, has attracted much attention as a key resource for applications including quantum information processing. In this thesis, we first develop a unifying framework based on non-Hermitian topology to understand non-reciprocity and directional amplification in driven-dissipative cavity arrays. Specifically, we unveil a one-to-one correspondence between a non-zero topological invariant defined on the spectrum of the dynamic matrix and regimes of directional amplification, in which the end-to-end gain grows exponentially with the number of cavities. Furthermore, we show that non-Hermitian topological amplification is robust against disorder as long as the disorder strength does not exceed the size of the point gap-the separation of the spectrum from the origin. In another part of this thesis, we revisit the bulk-boundary correspondence for non-Hermitian topological systems. It is a fundamental phenomenon of Hermitian topological phases, however, in non-Hermitian systems, it breaks down in the conventional form due to the non-Hermitian skin effect-the localisation of a macroscopic number of eigenvectors at the boundary. Here, we show that it is possible to restore the bulk-boundary correspondence by means of the singular value decomposition: when the system is topologically non-trivial, zero singular modes emerge leading to directional amplification with their number given by the topological invariant. In the final part, we extend the notion of non-reciprocity to unidirectional bosonic transport in time-reversal symmetric systems by exploiting interference between beamsplitter and two-mode-squeezing interactions. We develop a framework to identify the phenomenon we dub quadrature non-reciprocity based on features of the particle-hole graph representing the equations of motion. In addition to unidirectionality, these networks can exhibit an even-odd pairing between collective quadratures and an exponential end-to-end gain in the case of arrays of cavities. Our work opens up new avenues for signal routing, non-Hermitian topology, and amplification in bosonic systems.

In this thesis we examine several improvements which can be made to the canonical under- standing of Galactic Chemical Evolution (GCE) models in light of modern developments in stellar physics and new modelling techniques. Not only is GCE a vital component of our understanding of the history and composition of the universe in its own right, but since it incorporates physics on the scale of the cosmological to the subatomic, it may also be used as an independent probe and constraint on physics across many different fields. We develop two brand new, state-of-the-art models for studying galactic chemical evo- lution under two differing paradigms: the Simple Analytical Chemical Evolution Model (sacem) which allows for rapid and complete scans of the high-dimensional parameter space associated with GCE, and the updated version of the Radial Migration in Chemical Evolution Simulation (RAMICES II), which emulates the underlying physics chemical evolution as faithfully, and completely, as possible. These models allow us to investigate the origin of r-process nucleosynthesis within the Milky Way, in particular, identifying the ability of 'collapsar' events to contribute meaningfully to the global r-process budget. Utilising the sacem code, we are able to evaluate in excess of 10¹² potential models of the galaxy, and evaluate them against intentionally weak constrains on the resulting chemical and temporal properties, and hence provide a strong upper bound on the ability of such events to contribute to the r-process abundance of the Milky Way at late times. We study the impact of advances in stellar evolution modelling on GCE models, utilising new rotationally-resolved stellar evolution codes and nucleosynthetic yield grids. We show that the output from these new stellar models is fundamentally irreconcilable with observed data, and hence develop a number of tools which allow future stellar modelling to be rapidly diagnosed as incompatible, providing a new constraint on the internal evolution of stellar bodies. Finally, we apply our new RAMICES II model to briefly study the phenomena of metallicity- offset, strongly peaked curves in the gas-phase abundance diagrams - so called 'caustics' - and how these imprint themselves in non-trivial ways on the stellar abundance plane, using them to inform future studies of both r-process nucleosynthesis and the assembly history of the galaxy.

The aim of this thesis is to explore new constructions in supergravity to gain insights into the AdS₄/CFT₃ and AdS₅/CFT₄ correspondences. We start by deriving a simple formula for the action of any supersymmetric solution to minimal gauged supergravity in the AdS₄/CFT₃ correspondence. We find that the holographically renormalized action localizes to the fixed points of a supersymmetric Killing vector and may then be expressed entirely in terms of topological data. In this sense, the gravitational partition function localizes in the bulk. Our general formula reproduces all known examples in the literature and makes predictions for new solutions, assuming they exist. Also in D=4, N=2 minimal gauged supergravity, we sudy a class of accelerating, rotating and dyonic black holes in AdS₄. When the acceleration is non-vanishing, These D=4 black hole metrics have conical singularities but we find a new way to desingularize them by uplifting to solutions of D=11 supergravity using a regular Sasaki-Einstein SE₇ manifold. These D=11 solutions are associated to M2-branes wrapped around a two-dimensional weighted projective space, WCP¹[ₙ₋,ₙ₊], also known as a spindle, and we find that supersymmetry is not preserved through a usual topological twist. We also discuss the supersymmetric and extremal limits of these solutions and compute the entropy of these black holes, arguing that it should be possible to derive it from certain N=2, d=3 quiver gauge theories compactified on a spinning spindle with magnetic flux. In the AdS₅/CFT₄ correspondence we continue exploring these ideas by constructing AdS₃ x WCP¹[ₙ₋,ₙ₊] solutions of different D=5 supergravity theories. Again we find that these solutions can be uplifted to find smooth solutions in D=10/11 and that supersymmetry is preserved in a different way than through the topological twist. Our construction suggests a path to the dual d=2, N=(0,2) SCFTs in the IR, associated to D3 or M5 branes wrapped on a spindle. We make a precision test of this conjecture by computing the central charge and R-symmetry of the field theories and find agreement with the gravity computations in all cases.

Shannon's theory of information laid the groundwork for the rapid developments in information and communications technologies over the last century. Yet, it assumed that information carriers were described by the laws of classical physics, whilst at the most fundamental level, nature obeys the laws of quantum physics. Quantum Shannon theory, which describes information carriers as quantum states, has led to a new era of possibilities, such as perfectly secure cryptography without pre-established keys. Yet, there is a sense in which this transition from classical to quantum is incomplete. Traditionally, quantum Shannon theory has focused on scenarios where the internal states of information carriers are quantum, whilst their trajectories in spacetime have still been assumed to be classical. This work presents a second level of quantisation where both the information itself and its propagation in spacetime are treated in a quantum fashion. The second-quantised Shannon theory describes the possibility of a single particle being simultaneously transmitted through multiple communication channels in a quantum superposition. The framework is developed using the tools of higher-order transformations and quantum resource theories, formally quantifying the resources required for communication between a sender and receiver in this setting. The advantages of the second-quantised theory are illustrated in a series of examples, showcasing various counterintuitive phenomena that occur when information is simultaneously transmitted through multiple communication channels. In particular, when a single particle travels in a quantum superposition through two alternative transmission lines, the noisy processes in the two lines can destructively interfere, leading to a cleaner communication channel overall. Various different scenarios are encompassed in the framework, including transmission through a superposition of both independent and correlated channels, as well as through large-scale communication networks. This work concludes with a study of the robustness of these protocols to errors and a discussion of recent experimental demonstrations of their associated communication advantages.

This thesis details studies into soft and collinear radiation dressing QCD hard process amplitudes. Primarily, we present a formalism which reduces the computation of arbitrary multiplicities of soft and collinear QCD radiation in the massless limit, dressing any QCD hard process, to a single Markovian evolution equation. We present the evolution equation at leading logarithmic order, with complete spin correlations, and notably without approximating the QCD colour charge; though our formalism can be systematically extended beyond this order. We investigate the formalism and find that it can be used to study the accuracy of modern day parton showers, motivate new parton showers with increased accuracy, and study the factorisation properties of QCD processes in hadron colliders. From our studies, we introduce a new form of dipole shower, constructed to inherit the accuracy of an angular-ordered shower without losing the benefits and generalised applicability of a traditional dipole shower. We also study observables which suffer from coherence violating logarithms in proton evolution at hadron colliders. We arrive at the conclusion that almost all observables at hadron colliders will violate coherence to some degree. Only observables entirely insensitive to wide-angle soft physics remain completely safe. This thesis consists of five individual publications and supplementary material providing context and greater detail. This thesis is also supplemented with an extended discussion of introductory material on quantum chromodynamics and quantum field theories more broadly.

We examine three topics in the physics of three-dimensional systems, paying particular attention to the roles of topological field theory, topological solitons, and duality. First, we consider the dynamics of nonrelativistic Chern--Simons-matter theories in $2+1$ dimensions. The theories we consider support vortex solutions and, at critical coupling, they admit an effective low-temperature description as a topological quantum mechanics on the moduli space of these vortices. Using localisation techniques, we compute the 'expected' dimension of the Hilbert space of this quantum mechanics (that is, the Euler characteristic of the relevant quantum line bundle on the moduli space) in the case of $U(N_c)$ gauge theory with $N_f$ fundamental flavours at arbitrary Chern--Simons level, $\lambda$, compactified on an arbitrary closed Riemann surface. We apply this result to the analysis of the duality between the vortices of these theories and the (composite) fermions that arise in descriptions of strongly correlated electron systems and, in particular, of (nonAbelian, fractional) quantum Hall fluids. In simple cases, where the degeneracies of the fermion fluids are well understood, the results give quantitative evidence for these dualities. For example, when $N_c = N_f = \lambda$ we find strong evidence that the vortices are dual to fermions in the lowest nonAbelian Landau level associated to a background $U(N_f)$ flux. In more complicated examples, the results lead us to quantitative insight into the conjectural dual theory. We find that quantum vortices generally admit a description as composite objects, bound states of (dual) anyons. We comment on potential links with three-dimensional mirror symmetry. We also compute the equivariant expected degeneracy of local Abelian vortices on the $\Omega$-deformed sphere, finding it to be a $q$-analog of the undeformed version. By taking the semiclassical limit, we use our result to compute the volumes of vortex moduli spaces (which are closely related to the statistical mechanical partition functions of vortex gases). The volume of the $k$-vortex moduli space is a polynomial in the volume of physical space and, in the local case of $N_c = N_f$, we find a reduction in the degree of this polynomial, from $N_f k$ to $k$, resolving a point of confusion in the literature. We also find new integrability results relating solutions of the exotic vortex equations, which generalise the Jackiw--Pi and Ambjørn--Olesen vortex equations, in theories with $N_f=1$ to pairs consisting of a flat $PSU(N_c+1)$ connection and a holomorphic section of the associated holomorphic $\mathbb{C}P^{N_c}$-bundle. As well as providing a way to generate exact exotic vortex solutions in nonAbelian gauge theories, this leads to conjectural descriptions of the moduli spaces of exotic vortices and to topology-dependent selection rules for exotic vortex solutions (generalising the fact that Jackiw--Pi vortex solutions on the infinite sphere always have even flux). Second, we turn our attention to three-dimensional sigma models with $\mathcal{N}=4$ supersymmetry. When its target space is a hyperKähler manifold carrying a (so-called) permuting $Sp(1)$ action, such a sigma model admits two topological twists: the A-twist and the B-twist. The B-twist, also known as Rozansky--Witten theory, is well-understood, while the A-twist is a little more mysterious. The two twists are expected to be related by three-dimensional mirror symmetry. We construct the A-twist on general three-manifolds and analyse its local and extended operators. We show that compactifying the theory on a circle gives the two-dimensional A-model in the presence of a certain 'defect operator'. We then outline the construction of the 2-category of boundary conditions in the three-dimensional A-twist. In particular, we find that the A-twist induces a monoidal structure on the Fukaya categories of a certain, restricted, class of Kähler manifolds. Third, we consider magnetic Skyrmions in ferromagnetic materials. We produce a continuum toy model of fractionalised electrons in three spatial dimensions describing magnetic Skyrmions and their creation and destruction via emergent magnetic monopoles. When an external magnetic field is applied, the model has a critical point where confined monopoles are dynamically stabilised and monopole-antimonopole pairs may condense. We find novel 'BPS-like' equations for these configurations. By tuning the model to critical coupling and then deforming it, we find qualitative agreement with the observed phase structure of chiral ferromagnets. We then consider the critically-coupled model for magnetic Skyrmions on thin films, generalising it to thin films with curved geometry. We find exact Skyrmion solutions on some curved films with symmetry, namely spherical, conical, and cylindrical films. We prove the existence of Skyrmion solutions in the model on general compact films and investigate the geometry of the (resolved) moduli space of solutions.

In quantum gravity and field theory, large gauge transformations lead to novel degrees of freedom living at the boundary. In the presence of a black hole they are called ‘soft hair’, and it has been suggested that they go some way towards answering the black hole information problem. More generally, they are known as ‘edge modes’, and play a key role in the structure of the quantum state. Another approach to black hole information involves entanglement, and a key theme of this thesis is to explore aspects of the relationship between edge modes and entanglement. We first establish a thermodynamical interpretation of soft hair by deriving generalisations of the laws of black hole mechanics. These laws lead to a natural definition of an entropy density on the black hole horizon, and reveal that soft hairs at neighbouring points are in thermal contact with one another. There are boundary ambiguities in the traditional construction of phase spaces in field theory, and resolving these ambiguities is a step that must be taken before one can fully understand edge modes and soft hair. We provide two possible approaches to such a resolution. The first approach applies to theories without gravity, and involves a direct evaluation of the Poisson structure from a semiclassical path integral. This is then inverted to give the symplectic structure. The second approach applies in holographic theories of quantum gravity. We show how one can recover the symplectic structure in a bulk subregion by measuring an object known as ‘Uhlmann holonomy’ on the boundary, which is a generalisation of Berry phase. The Uhlmann holonomy is actually a direct measure of the entanglement in the quantum state, and so this provides a connection between edge modes and entanglement. In the final part of the thesis we study Uhlmann phase more generally, showing that it may be computed with a holographic path integral in a generic system, so long as the state of the system involves a sufficient degree of entanglement. This suggests that there are deep connections between Uhlmann holonomy, entanglement and holography.

Cosmic strings are a fundamental feature of many physically-motivated field theories which inevitably form in the early Universe, as a result of a symmetry breaking phase transition. An important example is the Peccei-Quinn mechanism, from which strings emerge as a potential source of dark matter axions. They are also a strong source of gravitational wave (GW) emission, with the potential for detection by the Laser Interferometer Gravitational-Wave Observatory (LIGO) and other GW experiments. The nonlinear evolution of cosmic strings has been extensively studied using large-scale numerical simulations. However, the vast difference in scale between a typical string width and the string curvature poses a significant computational challenge. This is usually addressed by approximating the string to have either zero or fixed comoving width, resulting in inconsistencies in predictions between different methods. One technique that can address this issue is adaptive mesh refinement (AMR), which allows the resolution of the numerical grid to adapt to the scale of the features of interest in the simulation. This thesis uses GRChombo, a sophisticated code originally designed for numerical relativity, to perform the first AMR simulations of global cosmic strings. We also present our numerical contributions to GRChombo as a core developer, including novel diagnostic tools and performance enhancement. We perform a detailed quantitative investigation of single sinusoidally displaced string configurations, comparing oscillating string trajectories with a backreaction model accounting for radiation energy losses. We conclude that analytic radiation modelling in the thin-string (Nambu-Goto) limit provides the appropriate picture for cosmological evolution. We also investigate the resulting massless (Goldstone boson or axion) and massive (Higgs) radiation signals, using quantitative diagnostic tools to determine their eigenmode decomposition. We find that the massless quadrupole is dominant and massive radiation is strongly suppressed with increasing mass, with a complex wavepacket structure that is sensitive to numerical resolution. String network configurations are also simulated, with advanced visualisation of radiation used to reveal new qualitative phenomena as strings reconnect and small loops decay. The thesis concludes with the cosmological implications of this work, considering dark matter axions radiated by cosmic strings and the outlook for gravitational wave signatures.

Light scalar fields emerge as a generic prediction in physics beyond the Standard Model. For example, they arise as new degrees of freedom in modified gravity, as Kaluza-Klein modes from extra compactified dimensions, and as Nambu-Goldstone bosons from spontaneously broken symmetries. Far from being just objects of theoretical interest, these scalar fields could also play crucial roles in resolving some of the most important open problems, such as the nature of dark matter and dark energy. Given this ubiquity in modern theoretical physics and their potentially far-reaching implications, efforts to detect or otherwise rule out these hypothetical scalars have burgeoned into a global enterprise in recent years. This thesis contributes to this ongoing effort by updating our understanding of how light scalar fields influence the dynamics of moving bodies, focusing on two novel scenarios. We begin by reanalysing the motion of electrons in laboratory experiments designed to deliver high-precision measurements of the fine-structure constant. The vacuum chambers employed in these setups make them ideal testing grounds for a class of scalar--tensor theories that screen the effects of their scalar mode based on the ambient density. If unscreened, the scalar exerts an attractive “fifth” force on the electron and, moreover, transforms the vacuum cavity into a dielectric medium due to its interactions with electromagnetic fields. Because these effects introduce different amounts of systematic bias into each experiment, good agreement between independent measurements of the fine-structure constant can be used to establish meaningful constraints on the parameter spaces of these models. In the second part of this thesis, we turn to investigate how ambient scalar fields influence the motion of binary black holes. Even though the models we consider are subject to no-hair theorems, the interplay between absorption at the horizons and momentum transfer in the bulk of the spacetime still gives rise to interesting phenomenology. We show that this interaction causes a fraction of the ambient field to be ejected from the system as scalar radiation, while the black holes themselves are seen to feel the effects of an emergent fifth force. Moreover, if the ambient field corotates with the binary, it can extract energy from the orbital motion and grow exponentially through a process akin to superradiance. Although these effects turn out to be highly suppressed in the regime amenable to analytic methods, the novel techniques developed herein lay the groundwork for future studies of these complex gravitational systems.

The Large-Scale Structure (LSS) of the Universe, i.e. the distribution of matter and luminous tracers (such as galaxies), contains a wealth of information about the origin, composition, and evolution of the Universe. In order to extract this information, the non-linearities present in late-time observables provided by LSS surveys must be understood well. In general, there are three main sources of non-linearities: (1) non-linear matter clustering due to gravity; (2) non-linear biasing, i.e. the relation between the distribution of tracers and dark matter; and (3) primordial non-Gaussianity, which induces non-linearities in the initial conditions. The Effective Field Theory of Large-Scale Structure (EFTofLSS) provides a powerful framework to model the non-linear clustering due to gravity. In this thesis, we focus on understanding the non-linearities due to galaxy biasing using the EFTofLSS and numerical N-body simulations. This thesis is comprised of the following three projects: In the first part, we present a novel method to constrain quadratic and cubic galaxy bias parameters in dark matter simulations. The natural statistics to constrain quadratic and cubic bias parameters are tree-level bispectrum and trispectrum, respectively. Since these statistics are computationally quite expensive, we use efficient squared and cubic field estimators that contain integrated bispectrum and trispectrum information. We use the constraints to model the one-loop halo-matter power spectrum and show that the results agree with simulations up to kmax = 0.1h Mpc 1 once an additional derivative bias is implemented (Published in: Abidi & Baldauf, JCAP07(2018)029). In the second part, we develop a formalism to reconstruct the linear density field based on quadratic couplings in galaxy clustering. We employ a quadratic estimator inspired by Cosmic Microwave Background (CMB) lensing reconstruction. We incorporate non-linearities due to gravity, galaxy biasing and primordial non-Gaussianity, and verify our predictions with N-body simulations. We perform a Fisher matrix analysis on how the reconstructed field in combination with the biased tracer field can improve constraints on local type primordial non-Gaussianity. We find significant improvement on constraints due to cosmic variance cancellation resulting from the additional correlated modes of the reconstructed field, similar to multi-tracer analyses. In the third part, we develop a method to constrain non-linear galaxy bias parameters using the two- and three-point functions of projected galaxy clustering in correlation with CMB lensing convergence. The project thus aims to bring the methodology developed in project 1 above closer to data. We develop the quadratic field method for projected fields to avoid complications from non-linear redshift space distortions. We perform a Fisher forecast to show that this method can indeed be used to put constraints on bias parameters and the amplitude of matter fluctuations. Finally, using N-body simulations we ascertain that the projected statistics do indeed reduce the impact of finger-of-god corrections.

In this thesis we explore Einstein gravity coupled to matter, and more specifically, we focus on the Kerr black hole in the presence of a massive scalar field. We investigate the superradiant phenomenon present in this setting - amplified scattering of scalar waves by the black hole given the right conditions on the scalar field's frequency are satisfied. Due to the mass term the spacetime develops a trapping region where the scalar waves can get localised instead of dispersing to infinity. In this way, the energy extracted from the black hole leads to the formation of a quasi bound state of the scalar field around it, known as a scalar cloud. This parallels the situation in Kerr-AdS, where due to the timelike character of the boundary this phenomenon appears more naturally and one does not necessarily need to make the field massive. We explore some of the consequences due to the formation of the scalar clouds in the asymptotically flat context. In the case of a complex scalar field the configuration can actually settle to a stationary solution to the Einstein equation which represents a scalar hairy Kerr black hole in asymptotically flat four dimensions - the first example of such black holes that does not violate energy conditions, discovered recently. These scalar hairy black holes branch off from the Kerr solution at the onset of scalar superradiance, when the scalar cloud starts forming. Since their discovery a number of studies have been carried out, trying to relate their properties to astrophysics. However, prior to our work, no stability analysis was performed. This is particularly important if we want to argue for the astrophysical significance of such solutions. We made the initial step in answering this question by showing that such black holes are unstable towards higher excited superradiant modes than the mode from whose onset they branched off. This required the construction of the black hole backgrounds numerically, utilising the DeTurck method and solving a system of PDEs with extended precision using spectral methods. Afterwards, a clever choice of gauge allowed us to decouple the scalar field perturbations form the gravitational sector and perform the analysis by looking at the quasinormal mode spectrum of the hairy solutions. When the scalar field is real, these stationary hairy solutions do not exist, but scalar clouds still form around the black hole. Moreover, our previous work suggested that for any parameters of the Kerr black hole, an unstable scalar mode will be present. We showed this analytically using a hybrid WKB and matched asymptotic expansion technique and confirmed it with numerical data. This led us to explore an idea for a plausible counterexample to the Weak Cosmic Censorship Conjecture in flat four dimensions, based on the cascading of energies, as seen in AdS, whereby with time even higher superradiant modes become dominant and form clouds around the black hole. In support of our claim we have integrated the sourced Teukolsky equation for gravitational perturbations of Kerr numerically with extended precision in order to obtain the backreaction of the scalar field on the geometry and also analysed the system analytically, as detailed above, in order to confirm our numerics and discuss the endpoint of the evolution of the system.

Ultracold atomic gases loaded into optical cavities constitute one of the most versatile platforms for the study of out-of-equilibrium dynamics and quantum simulation of many- body systems. In this thesis, we explore these two possibilities, motivated by current state-of-the-art atom-cavity experiments, uncovering novel phenomena and opening up new theoretical and experimental avenues into the intriguing world of quantum many- body physics. First, we study a gas of ultracold atoms coupled to three optical resonators. We show that the inherent Z2 symmetries, associated with each atom-cavity coupling, can be combined into a global SO(3) rotational symmetry which can be spontaneously broken. We determine the phase diagram of the system, which shows the emergence and breaking of the continuous symmetries and displays first- and second-order phase transitions. We argue that by coupling the atoms equally to n different modes, it will in general be possible to generate a global SO(n) symmetry. Second, we investigate the dynamics of a spinor BEC inside an optical cavity. We focus on a two-component Dicke model with complex light-matter couplings, accounting for photon losses. We compute the steady-state phase diagram and find dynamical in- stabilities in the form of limit cycles, heralded by the presence of exceptional points and level attraction. We show that the instabilities are induced by dissipative processes that generate nonreciprocal couplings between the two collective spins. Lastly, we explore the dynamics of a BEC inside an optical cavity in the presence of an optical lattice. We derive an effective master equation by adiabatically eliminating the cavity field. In the bad-cavity regime, we find an infinite-temperature steady state, but with relaxation dynamics that can be highly nontrivial. For small hopping, the interplay between dissipation and strong interactions leads to an algebraic relaxation of the system, whereas for large hopping, the approach to the steady state is exponential. In the good- cavity regime, we show that the system allows for optical pumping between momentum modes, enabling cavity cooling.

Cosmological inflation is a simple, and observationally well-supported, mechanism for generating a flat, spatially homogeneous universe with the statistical correlations in the cosmic microwave background we see today. Determining precisely how inflation happened, and how many fields were involved, are some of the main challenges of modern cosmology. The first part of the thesis, consisting of Chapters 2 and 3, addresses this question by looking at what future measurements of local non-Gaussianity will tell us. Local non-Gaussianity has been proposed as a key observable for distinguishing between single- and multifield inflation, as a large value of this parameter would rule out the former. However, a small value would not necessarily rule out the latter. Using a new technique for generating random functions with Gaussian random fields, which we also prove the validity of, we generate random potentials for as many as 100 fields for inflation. We look at the observables of these models and in particular compute the local non-Gaussianity. An overwhelming majority of these models give local non-Gaussianity compatible with single-field inflation, despite significant multifield effects on superhorizon scales, indicating that this observable may not be sufficient to distinguish between these types of models. The second part of the thesis, consisting of Chapters 4 and 5, addresses another aspect of this question by looking at other types of inflationary solutions than slow-roll, slow-turn. Slow-roll, slow-turn is an easily realised solution, but requires a very flat potential over large distances in field-space. The fine-tuning needed for this remains an Achilles heel of the inflationary paradigm. However, there are inflationary solutions which can be realised in steep potentials. `Hyperinflation' is a particularly interesting one of these, and we investigate this solution in detail. Using the techniques developed to study hyperinflation, we then show that there exists a new, completely general two-field attractor solution that is characterised by rapidly turning fields. This `rapid-turn attractor' does not require any particular background geometry, and explains how several recently studied two-field inflation models are related to each other.

Lovelock and Horndeski theories are natural generalisations of Einstein’s theory of General Relativity. They find applications in Astrophysics, Cosmology and String Theory. This dissertation discusses some issues regarding the mathematical consistency of these theories. In the first part of the thesis we study the Shapiro time delay for gravitons in spherically symmetric spacetimes in Einstein–Gauss–Bonnet gravity (a Lovelock theory). In Lovelock theories, gravitons can propagate faster or slower than light. We show that, thanks to this property, it is possible for them to experience a negative time delay. It was recently argued that this feature could be employed to construct closed causal curves, implying that the theory should be discarded as causally pathological. We show that this construction is unphysical, for it cannot be realised as the evolution of sensible initial data. The second part investigates the local well-posedness of the initial value problem for Lovelock and Horndeski theories. For the initial value problem to be well-posed it is necessary that the equations of motion be strongly hyperbolic. It is known that when the background fields are large, even weak hyperbolicity may fail. Hence, we consider the weak field regime, in which these equations can be considered as small perturbations of the Einstein equations. We prove that both Lovelock and Horndeski theories are weakly hyperbolic in a generic weak field background in harmonic and generalised harmonic gauge, respectively. We show that Lovelock theories fail to be strongly hyperbolic in this setting. We also prove that the most general Horndeski theory which is strongly hyperbolic is simply a “k-essence” theory coupled to Einstein gravity and that any more general theory would necessarily fail to be so. Our results imply that the standard methods used to prove the well-posedness of the initial value problem for the Einstein equations cannot be extended to Lovelock or Horndeski theories. This raises the possibility that these theories may not admit a well-posed initial value problem even for weak fields and hence might not constitute a valid alternative to General Relativity.

The ΛCDM model for the Universe is highly successful in explaining cosmological observations to date, and its parameters tightly constrained by Cosmic Microwave Background (CMB) experiments such as Planck. Higher-order statistics, like the three-point correlation function or bispectrum in Fourier space, will be indispensable for furthering our understanding of the Universe. While these methodologies have been developed over the years and applied to CMB analyses, similar work on large-scale structure is still in its infancy. Additionally, information from future galaxy surveys such as LSST and Euclid will soon exceed that available from the CMB, demonstrating a pressing need for such tools. The theoretical modelling of non-linear gravitational interactions is difficult beyond the perturbative regime, necessitating large, expensive N-body dark matter simulations to understand the small-scale dynamics. Additionally, the direct numerical computation of the matter bispectrum is intractable due to the multiplicity of triangular configurations. In this Thesis, we make breakthroughs in both of these problems. First, we present the newly rewritten MODAL-LSS formalism that enables efficient and optimal estimation of the full bispectrum for any matter density field to unprecedented accuracy, as well as demonstrating rapid convergence which makes it ideal for the analysis of large datasets. This has allowed us to benchmark fast dark matter codes (e.g. particle-mesh or L-PICOLA) against GADGET-3 using the bispectrum, showing quantitatively how the mismatch at large k can be improved with a simple boosting technique in the power spectrum. We have also estimated the non-Gaussian contribution to the dark matter bispectrum covariance, which cannot be computed analytically in the non-linear regime. This will be vital for the extraction of cosmological parameters from data in the future. In preparation for the analysis of future galaxy datasets we have also investigated the non-trivial problem of linking the underlying dark matter density field to the observed galaxy distribution. As an important milestone we have investigated the effects of the halo profile, the Halo Occupation Distribution (HOD) model, and multivariate assembly bias models of the halo occupation and concentration on the power spectrum and full bispectrum of a subhalo catalogue derived from the ROCKSTAR halo finder. These fast, phenomenological methods allow us to pave the way for the efficient generation of mock galaxy catalogues.

In this thesis we consider the motion of a charged particle in strong electromagnetic background fields, having in mind applications to state-of-the-art high-power lasers. To find solutions of the Lorentz force equation of motion, we make use of Noether's theorem to identify conserved quantities of the charge dynamics. We will explain how, given enough symmetries, a dynamical system becomes integrable or, with a maximum number of conserved quantities, maximally superintegrable. Beginning with charged particles in vector background fields, we shall show that the relevant symmetry group is the Poincaré group. The dynamics for constant and univariate fields is classified, and their integrability properties are clarified. We then move on to the problem of a particle in a scalar background field and show that the symmetry group is extended to the conformal group. We then present examples of fields which include Poincaré, dilation and special conformal symmetries leading to varying extents of integrability.

Holographic dualities are now an established tool in the study of universal properties of strongly coupled field theories. Yet, theories without translational symmetry are still poorly understood in this context. In this dissertation, we investigate three new approaches to this challenging problem. The first part of the dissertation concerns a class of phenomenological holographic models in which momentum relaxation can be achieved without breaking translational symmetry in the dual geometry. In particular, we focus on an example in which the dual geometry is similar to anti-de Sitter (AdS) Brans-Dicke theory. We study the thermodynamic and transport properties of the model and show that for strong momentum relaxation and low temperatures the model has insulator-like behaviour. In the second part, we go beyond the effective description and consider holographic theories which explicitly break translational symmetry. From the perspective of gravity, these theories translate to geometries that vary explicitly in the boundary space-like coordinates. We refer to these geometries as 'inhomogeneous' and investigate two approaches to study them. The first is motivated by the question: "what happens to a homogeneous geometry when coupled with a field varying randomly in space?". Starting from an AdS geometry at zero or finite temperature, we show that a spatially varying random Maxwell potential drives the dual field theory to a non-trivial infra-red fixed point characterised by an emerging scale invariance. Thermodynamic and transport properties of this disordered ground state are also discussed. The second is motivated by the complementary question: "how does a random geometry affect a probe field?". In the weak disorder limit, we show that disorder induces an additional power-law decay in the dual correlation functions. For certain choices of geometry profile, this contribution becomes dominant in the infra-red, indicating the breaking of perturbation theory and the possible existence of a phase transition induced by disorder. The third and last part of this dissertation switches from the gravity to the field theoretical side of the duality. We discuss the Sachdev-Ye-Kitaev (SYK) model, a disordered many-body model with distinctive black hole-like properties. We provide analytical and numerical evidence that these holographic properties are robust against a natural one-body deformation for a finite range of parameters. Outside this interval, this system undergoes a chaotic-integrable transition.

One of the primary targets of current and especially future cosmological observations are light thermal relics of the hot big bang. Within the Standard Model of particle physics, an important thermal relic are cosmic neutrinos, while many interesting extensions of the Standard Model predict new light particles which are even more weakly coupled to ordinary matter and therefore hard to detect in terrestrial experiments. On the other hand, these elusive particles may be produced efficiently in the early universe and their gravitational influence could be detectable in cosmological observables. In this thesis, we describe how measurements of the cosmic microwave background (CMB) and the large-scale structure (LSS) of the universe can shed new light on the properties of neutrinos and on the possible existence of other light relics. These cosmological observations are remarkably sensitive to the amount of radiation in the early universe, partly because free-streaming species such as neutrinos imprint a small phase shift in the baryon acoustic oscillations (BAO) which we study in detail in the CMB and LSS power spectra. Building on this analytic understanding, we provide further evidence for the cosmic neutrino background by independently confirming its free-streaming nature in different, currently available datasets. In particular, we propose and establish a new analysis of the BAO spectrum beyond its use as a standard ruler, resulting in the first measurement of this imprint of neutrinos in the clustering of galaxies. Future cosmological surveys, such as the next generation of CMB experiments (CMB-S4), have the potential to measure the energy density of relativistic species at the sub-percent level and will therefore be capable of probing physics beyond the Standard Model. We demonstrate how this improvement in sensitivity can indeed be achieved and present an observational target which would allow the detection of any extra light particle that has ever been in thermal equilibrium. Interestingly, even the absence of a detection would result in new insights by providing constraints on the couplings to the Standard Model. As an example, we show that existing bounds on additional scalar particles, such as axions, may be surpassed by orders of magnitude.

Feynman diagrams have been superseded as the tool of choice for calculating scattering amplitudes. Various other methods are not only more efficient but also explicitly exhibit beautiful structures obscured by Feynman diagrams. This thesis aims to lay some groundwork on how two of these methods, ambitwistor strings and the double copy, can be generalised to scattering in curved backgrounds. In the first part of this thesis, a heterotic ambitwistor string model coupled to a non-abelian background gauge field is constructed. It is shown that after decoupling gravity this model is anomaly free if and only if the background field is a solution to the Yang-Mills equations. A fixed gluon vertex operator for the aforementioned heterotic model as well as a vertex operator encoding graviton, B-field and dilaton for type II ambitwistor strings in a curved background are presented. It is shown that they are BRST closed if and only if they correspond to physical on-shell states. In the second part, sandwich plane waves are considered. It is shown that scattering of gluons and gravitons is well defined on these backgrounds. 3-point amplitudes are calculated using quantum field theory techniques and a double copy relation between gluons on a gauge theory plane wave and gravitons on a gravitational plane wave is proposed. Using the results from the first part of this thesis, it is then shown that curved background heterotic and type II ambitwistor string models correctly reproduce these 3-point amplitudes on sandwich plane waves.

The formulation of rigid supersymmetric field theories on curved space leads to a number of results on their strongly-interacting regime, crucial from both the mathematical and physical point of view, starting from Witten's topological twist of four-dimensional Yang-Mills theory. At the same time, strongly-coupled field theories may also be studied holographically via the AdS/CFT correspondence. The aim of this thesis is to study aspects of the holographic dictionary for supersymmetric theories on curved manifolds. A key aspect of the correspondence is the renormalization of gravity observables, which is realized via holographic renormalization. If the dual boundary field theory is supersymmetric, it is natural to ask whether this scheme is compatible with the rigid supersymmetry at the curved boundary. The latter requires specific geometric structures, and general arguments imply that BPS observables, such as the partition function, are invariant under certain deformations of these structures. We may then formulate a precise check of the holographic dictionary by asking whether the dual holographic observables are similarly invariant, as the free energy of the gauge theory is identified with the holographically renormalized supergravity action. In the first part of the thesis, we consider this question in N = 4 gauged supergravity in four and five dimensions for the holographic dual to the topological twists of N = 4 gauge theories on Riemannian three-manifolds and N = 2 gauge theories on Riemannian four-manifolds. We show that the renormalized on-shell action is independent of the metric on the boundary four-manifold, as required for a topological theory. We then go further, analyzing the geometry of supersymmetric bulk solutions. This allows us to show that the gravitational free energy of any smooth filling vanishes in both AdS4/CFT3 and AdS5/CFT4. In the second part of the thesis, we study the same question in minimal N = 2 gauged supergravity in four and five dimensions. In four dimensions we show that holographic renormalization precisely reproduces the expected field theory results for the dependence of the partition function on the background. Surprisingly, in five dimensions we find that no choice of standard holographic counterterms is compatible with supersymmetry, which leads us to introduce novel finite boundary terms. For a class of solutions satisfying certain topological assumptions we provide some independent tests of these new boundary terms, in particular showing that they reproduce the expected VEVs of conserved charges. We also briefly comment on the relation between these terms and boundary supercurrent anomalies.

Since the discovery of the cosmic microwave background (CMB), our understanding of the cosmos has been rapidly evolving. Detailed measurements of the CMB temperature fluctuations have led to a standard cosmological model, which traces the origin of the large-scale structure of the universe to quantum fluctuations during inflation. Although the basic framework of inflationary cosmology is now well-established, the microphysical mechanism responsible for the accelerated expansion remains a mystery. In this thesis, we describe how the physics underlying inflation can be probed using two cosmological observables: higher-order correlations of primordial density perturbations (non-Gaussianity) and primordial gravitational waves (tensor modes). In the first part of the thesis, we explore novel signatures of high-energy physics in higher- order correlation functions of inflationary perturbations. First, we use causality and unitarity to make connections between cosmological observations and the underlying short-distance dynamics of single-field inflation. We obtain a constraint on the size and the sign of the four-point function in terms of the amplitude of the three-point function. We then study the imprints of extra massive particles of arbitrary spin on the three-point function. We classify the couplings of these particles to inflationary scalar and tensor perturbations and derive explicit shape functions for their three- point functions that can serve as templates for future observational searches. Establishing the particle content during inflation would provide important hints for the microscopic theory of inflation. In the second part, we study ways of testing the nature of inflation using inflationary tensor modes. We consider effects of gravitational corrections to Einstein gravity in models of high-scale inflation. We show that these scenarios can lead to a violation of the tensor consistency condition (i.e. the relation between the amplitude and the scale-dependence of the tensor two-point function) that is satisfied by canonical single-field inflationary models. Finally, we consider the prospects for measuring the inflationary superhorizon signature in future observations. We define an estimator that captures superhorizon correlations and present forecasts for the detectability of the signal with future CMB polarization experiments.

We study three types of theories, using supersymmetry and ideas from string theory as tools to gain understanding of systems of more general interest. Firstly, we introduce non-relativistic Chern-Simons-matter field theories in three dimensions and study their anyonic spectrum in a conformal phase. These theories have supersymmetric completions, which in the non-relativistic case suffices to protect certain would-be BPS quantities from corrections. This allows us to compute one-loop exact anomalous dimensions of various bound states of non-Abelian anyons, analyse some interesting unitarity bound violations, and test some recently proposed bosonization dualities. Secondly, we turn on a chemical potential and break conformal invariance, putting the theory into the regime of the Fractional Quantum Hall Effect (FQHE). This is illustrated in detail: the theory supports would-be BPS vortices which model the electrons of the FQHE, and they form bag-like states with the appropriate filling fractions, Hall conductivities, and anyonic excitations. This formalism makes possible some novel explicit computations: an analytic calculation of the anyonic phases experienced by Abelian quasiholes; analytic relationships to the boundary Wess-Zumino-Witten model; and derivations of a wide class of QHE wavefunctions from a bulk field theory. We also further test the three-dimensional bosonization dualities in this new setting. Along the way, we accumulate new descriptions of the QHE. Finally, we turn away from flat space and investigate a problem in (3+1)-dimensional quantum gravity. We find that even as an effective theory, the theory has enough structure to suggest the inclusion of certain gravitational instantons in the path integral. An explicit computation in a minimally supersymmetric case illustrates the principles at work, and highlights the role of a hitherto unidentified scale in quantum gravity. It also is an interesting result in itself: a non-perturbative quantum instability of a flat supersymmetric Kaluza-Klein compactification.

Thermal and viscous forces compete for dominance at the microscopic length-scales which govern the behaviour of many soft or biological systems. We study three systems of increasing complexity with the central goal of understanding the statistical or hydrodynamic nature of their mechanics. First we study experiments that have been conducted on ferromagnetic colloidal rods. At equilibrium, the magnetically pinned rod is observed to randomly flip between two orientational states, which our theoretical analysis shows is due to a competition between entropic and Hamiltonian forces. We show analytically how entropic forces can arise by considering the coupling between observed and unobserved variables of a system. Experiments in which a rod is driven out of equilibrium by a rotating field display three phases of steady-state behaviour as a function of driving frequency. Using Brownian dynamics simulations we match the lower critical frequency to the experimentally obtained values, showing that thermal fluctuations play an important role in this regime and propose a simple argument to demonstrate that hydrodynamic interactions between the substrate and rod affect the upper critical frequency. We then turn to the biophysical topic of cell locomotion in viscoelastic media. In order to study how bacterial flagella interact with similarly-sized polymers in their environment, we construct a Stokesian dynamics model of a helical filament and bead--spring polymer. Simulating their interaction first for a pinned--rotating helix, then for a swimming helix, we demonstrate that large polymers become hydrodynamically entrained by the flagellum and coil around it, causing both pinned and swimming flagella to expend more work. For the swimming helix, this results in a reduction of swimming speed on average. Finally, we consider an active nematic fluid confined to a channel and show that the inclusion of a passive colloid induces a global state of coherent flow maintained by the intrinsic activity of the system. This flow is persistent, and transports the colloid with it along the channel. By this mechanism, a passive colloid is able to spontaneously induce its own transport through an otherwise quiescent fluid.

In this thesis we explore various aspects of Calabi-Yau (CY) manifolds and com- pactifications of the heterotic string over them. At first we focus on classifying symmetries and computing Hodge numbers of smooth CY quotients. Being non- simply connected, these quotients are an integral part of CY compactifications of the heterotic string, aimed at producing realistic string vacua. Discrete symmetries of such spaces that are generically present in the moduli space, are phenomenologically important since they may appear as symmetries of the associated low energy theory. We classify such symmetries for the class of smooth Complete Intersection CY (CICY) quotients, resulting in a large number of regular and R-symmetry examples. Our results strongly suggest that generic, non-freely acting symmetries for CY quotients arise relatively frequently. A large number of string derived Standard Models (SM) were recently obtained over this class of CY manifolds indicating that our results could be phenomenologically important. We also specialise to certain loci in the moduli space of a quintic quotient to produce highly symmetric CY quotients. Our computations thus far are the first steps towards constructing a sizeable class of highly symmetric smooth CY quotients. Knowledge of the topological properties of the internal space is vital in determining the suitability of the space for realistic string compactifications. Employing the tools of polynomial deformation and counting of invariant Kähler classes, we compute the Hodge numbers of a large number of smooth CICY quotients. These were later verified by independent cohomology computations. We go on to develop the machinery to understand the geometry of CY manifolds embedded as hypersurfaces in a product of del Pezzo surfaces. This led to an interesting account of the quotient space geometry, enabling the computation of Hodge numbers of such CY quotients. Until recently only a handful of CY compactifications were known that yielded low energy theories with desirable MSSM features. The recent construction of rank 5 line bundle sums over smooth CY quotients has led to several SU(5) GUTs with the exact MSSM spectrum. We derive semi-analytic results on the finiteness of the number of such line bundle models, and study the relationship between the volume of the CY and the number of line bundle models over them. We also imply a possible correlation between the observed number of generations and the value of the gauge coupling constants of the corresponding GUTs. String compactifications with underlying SO(10) GUTs are theoretically attractive especially since the discovery that neutrinos have non-zero mass. With this in mind, we construct tens of thousands of rank 4 stable line bundle sums over smooth CY quotients leading to SO(10) GUTs.

This thesis investigates applications of the gauge/gravity duality to strongly coupled quantum field theories. After a review of the duality and of correlators and transport in quantum systems, we present our results on second-order non-conformal hydrodynamics. We derive new Kubo formulae for five second-order transport coefficients in non-conformal relativistic fluids. We then apply these Kubo formulae to a class of non-conformal holographic fluids at infinite coupling. We find strong evidence that the Haack-Yarom identity, known to relate second-order coefficients in conformal holographic fluids at infinite coupling, continues to hold in holographic fluids without conformal symmetry: Within our class of models, we prove that it still holds when leading non-conformal corrections are taken into account, and we show numerically that it is also obeyed beyond leading order. This provides further evidence that the identity may be a universal feature of strongly coupled fluids. Next, we present our results on magnetic spin impurities in strongly correlated systems. We build a holographic two-impurity Kondo model, identifying the inter-impurity interaction as double-trace deformation. Our numerical results for the phase diagram suggest a quantum phase transition between a trivial phase with uncorrelated spins and no Kondo screening, and a non-trivial phase with anti-ferromagnetic correlations and simultaneous Kondo screening. Computing the spectrum in the single-impurity case, we observe Fano resonances, which at low temperatures we identify with the Kondo resonance.

The Standard Model of particle physics has enjoyed unprecedented success in predicting experimental results. However, evidence from astrophysical observations points to the existence of a dark sector of particles that interact only very weakly with the Standard Model. In this work, we search for dark sector signatures in X-ray telescope data. Much of this work concerns a class of hypothetical particles, the axion-like particle (ALP). ALPs are a theoretically well-motivated extension of the Standard Model. If ALPs exist, they may lead to intriguing astrophysical signatures: in the presence of a background magnetic field, ALPs and photons can interconvert. We could detect ALPs by searching for photon to ALP conversion. For example, photons produced by point sources in or behind galaxy clusters may convert to ALPs in the cluster's magnetic field. This could lead to observable spectral anomalies. Using this strategy, we place world leading bounds on the ALP-photon coupling. One potential signal of dark matter is an anomalous line in the spectra of galaxies and galaxy clusters. In 2014, an anomalous line was found at an energy of 3.5 keV. The nature and cause of this line is still under discussion. We analyse a scenario in which the 3.5 keV line arises from dark matter decay to ALPs, which interconvert with 3.5 keV photons in astrophysical magnetic fields. We further report an anomalous deficit at 3.5 keV in the spectrum of the Active Galactic Nucleus at the centre of the Perseus galaxy cluster. This motivates the study of a new model in which both features are caused by “fluorescent dark matter” which resonantly interacts with 3.5 keV photons. We analyse observations of Perseus at 3.5 keV to date, and show that they are well explained by this model. Further theoretical and experimental work is needed to discover or exclude fundamental physics effects in X-ray spectra.

In this thesis we study a number of geometric structures arising in the study of four-dimensional supersymmetric quantum field theories. We study properties and applications of so-called "spectral networks" on Riemann surfaces C, focusing in particular on the "abelianization map" which we use to produce special coordinate systems on moduli spaces of local systems on C. We generalize the classical Fenchel-Nielsen coordinates and utilize these coordinates to compute superpotentials, following and generalizing a conjecture of Nekrasov-RoslyShatashvili. Our first result is a computation of the higher rank spectral coordinates associated to certain "generalized Fenchel-Nielsen" networks, yielding explicit formulas for the trace functions on the moduli space with two "minimal" and two "maximal" punctures. We use this result to verify the NRS conjecture at the lowest order asymptotics for a prototypical SU(3) theory, and furthermore compute the 1-instanton correction in the SU(2) case, extending previous results. In the final chapter we include some partial results the author has obtained on the existence and uniqueness of abelianizations for certain classes of networks related to Grassmannians.

This thesis contains four studies of the effects of disorder and randomness on strongly correlated quantum phases of matter. Starting with an itinerant ferromagnet, I first use an order-by-disorder approach to show that adding quenched charged disorder to the model generates new quantum fluctuations in the vicinity of the quantum critical point which lead to the formation of a novel magnetic phase known as a helical glass. Switching to bosons, I then employ a momentum-shell renormalisation group analysis of disordered lattice gases of bosons where I show that disorder breaks ergodicity in a non-trivial way, leading to unexpected glassy freezing effects. This work was carried out in the context of ultracold atomic gases, however the same physics can be realised in dimerised quantum antiferromagnets. By mapping the antiferromagnetic model onto a hard-core lattice gas of bosons, I go on to show the importance of the non-ergodic effects to the thermodynamics of the model and find evidence for an unusual glassy phase known as a Mott glass not previously thought to exist in this model. Finally, I use a mean-field numerical approach to simulate current generation quantum gas microscopes and demonstrate the feasibility of a novel measurement scheme designed to measure the Edwards-Anderson order parameter, a quantity which describes the degree of ergodicity breaking and which has never before been experimentally measured in any strongly correlated quantum system. Together, these works show that the addition of disorder into strongly interacting quantum systems can lead to qualitatively new behaviour, triggering the formation of new phases and new physics, rather than simply leading to small quantitative changes to the physics of the clean system. They provide new insights into the underlying physics of the models and make direct connection with experimental systems which can be used to test the results presented here.

The prototypical exciton model of two interacting Dirac particles in graphene was analysed by Sabio et al, Phys. Rev. B 81, 045428 (2010), and it was found that in one of the electron-hole scattering channels the total kinetic energy vanishes, resulting in a singular behaviour. We show that this singularity can be removed by extending the quasiparticle dispersion, thus breaking the symmetry between upper and lower Dirac cones. The dynamics of an electron-electron pair are then mapped onto that of a single particle with negative mass and anisotropic dispersion. We show that the interplay between dispersion and repulsive interaction can result in the formation of bound, Cooper-pair-like, metastable states in double-layered hybrid structures. We analyse these states by calculating their binding energies, decay rates into the free- electron continuum and semiclassical trajectories. We also analyse the problem of bi-electron pairing with the inclusion of the two dominant many-body effects at zero temperature: screening of the Coulomb interaction by the Dirac sea, and reduction of the available phase space due to Pauli blocking of transitions into the states below the Fermi level. We show that these effects result in strong renormalization of the binding energy, but do not destroy the metastable states. Thus the binding energies are strongly dependent on the chemical potential owing to the combined effects of screening and Pauli blocking. Hence, the quasibound resonances can be tuned by electrostatic doping.

Theoretical predictions for generic multi-scale observables in Quantum Chromodynamics (QCD) typically suffer from large Sudakov logarithms associated with the emission of soft or collinear radiation, whose presence spoils the perturbative expansion in the coupling strength which underlies most calculations in QCD. A canonical way to improve predictions wherever these logarithms appear is to resum them to all perturbative orders, which can conveniently be achieved using Effective Field Theory (EFT) methods. In an age of increasing automation using computers, this task is still mostly performed manually, observable-by-observable. In this thesis we identify the 2-loop soft function as a crucial ingredient for the resummation of QCD Sudakov logarithms to Next-to-next-to-leading logarithmic (NNLL) accuracy in Soft-Collinear Effective Theory (SCET), for wide classes of observables involving two massless colour-charged energetic particles, such as dijet event shapes at lepton colliders, or colour singlet production at hadron colliders. We develop a method to evaluate these soft functions using numerical methods based on sector decomposition and the choice of a convenient parametrisation for the phase space. This allows the factorisation of all implicit (real emission) and explicit (virtual correction) divergences made manifest by dimensional and analytic regularisation. The regulator pole coefficients can then be evaluated numerically following a subtraction and expansion, and two computational tools are presented to perform these numerical integrations, one based on publicly available tools, the other based on our own code. Some technical improvements over naive straightforward numerical evaluation are demonstrated and implemented. This allows us to compute and verify two of three colour structures of the 2-loop bare soft functions for wide ranges of observables with a factorisation theorem. A number of example results - both new and already known - are shown to demonstrate the reach of this approach, and a few possible extensions are sketched. This thesis therefore represents a crucial step towards automation of resummation for generic observables to NNLL accuracy in SCET.

The mystery of dark matter (DM) is undeniably one of the greatest in modern physics. For decades, evidence has accumulated from astrophysical and cosmological experiments suggesting that the Universe contains a large amount of mass yet unaccounted for. In particular, present research indicates that approximately 84% of the total matter content in the Universe is non-baryonic DM. Together with the well-known limitations of the Standard Model of particle physics (SM), some of which could be remedied by theories which necessarily include additional particles, a particle physics solution to the DM problem is certainly well motivated. In this thesis the Large Hadron Collider (LHC) phenomenology of three models of DM is studied. In particular, the focus is on signals due to final states containing hadronic jets in association with a large amount of missing transverse energy, corresponding to DM which escapes detection. For the first model, it is found that studying events with one jet in the final state can allow constraints to be derived on the size of the couplings between DM and SM particles, but it is not possible to extract any information about the structure of the couplings. This motivates an analysis of events which feature two jets. For the second model, it is found that measurements of the azimuthal angular separation of these jets lead to contrasting distributions depending on the Lorentz structure of the interactions. These spectra are shown to be stable under various corrections and, more importantly, are clearly produced whether or not one performs the calculation using an effective field theory framework. For the third model, which differs from the first two in that DM now couples to the SM gauge bosons rather than the quarks, recent experimental searches are used to derive bounds on the fiducial cross sections for a variety of final states featuring missing transverse energy. This facilitates a comparison to be made between the various search strategies, identifying which of these most strongly constrain the operators under consideration. Considering the final state containing two jets, the azimuthal angular distributions are then plotted and are again found to be strongly dependent on the Lorentz structure of the underlying interactions. Prospects for the 14 TeV LHC run are then studied and it is found that a clear distinction between the spectra should be possible once 300 fb-1 has been collected.

Microorganisms have evolved in a low Reynolds number environment and have adapted their behaviour to its viscosity. Here, we consider some features of behaviour observed in microorganisms and use hydrodynamic models to show that these behaviours emerge from physical interactions, including hydrodynamic friction, hydrodynamic interactions and mechanical constraints. Swimming behaviour is affected by surfaces and observations of Vibrio cholerae show that it swims near a surface with two distinct motility modes. We develop a model which shows that friction between pili and the surface gives the two motility modes. The model is extended to study the behaviour of bacteria which are partially attached to a surface. Observations of Shewanella constrained by a surface show several different behaviours. The model shows that different degrees of surface constraint lead to different types of behaviour; the flexibility of the flagellar hook and the torque exerted by the flagellar motor also cause different behaviours. Near surface behaviour is important for understanding the initial stages of biofilm formation. Chlamydomonas swims using synchronous beating of its two flagella. A simple model of Chlamydomonas is developed to study motility and synchronisation. This model shows that the stability of synchronisation is sensitive to the beat pattern. Run-and-tumble behaviour emerges when we include intrinsic noise, without the need for biochemical signalling. The model is also used to show how observed responses of the flagella to light stimuli produce phototaxis. Finally we study hydrodynamic synchronisation of many cilia and consider the stability of metachronal waves in arrays of hydrodynamically coupled cilia. This thesis shows that physical interactions are responsible for many behavioural features and that physical models provide a useful technique for exploring open questions in biology.

It is argued that the geometric dual of a noncommutative operator algebra represents a notion of quantum state space which differs from existing notions by representing observables as maps from states to outcomes rather than from states to distributions on outcomes. A program of solving for an explicitly geometric manifestation of quantum state space by adapting the spectral presheaf, a construction meant to analyze contextuality in quantum mechanics, to derive simple reconstructions of noncommutative topological tools from their topological prototypes is presented. We associate to each unital C*-algebra A a geometric object--a diagram of topological spaces representing quotient spaces of the noncommutative space underlying A—meant to serve the role of a generalized Gel'fand spectrum. After showing that any functor F from compact Hausdorff spaces to a suitable target category C can be applied directly to these geometric objects to automatically yield an extension F∼ which acts on all unital C*-algebras, we compare a novel formulation of the operator K0 functor to the extension K∼ of the topological K-functor. We then conjecture that the extension of the functor assigning a topological space its topological lattice assigns a unital C*-algebra the topological lattice of its primary ideal spectrum and prove the von Neumann algebraic analogue of this conjecture.

Fractional Chern insulators (FCIs) are strongly correlated, topological phases of matter that may exist on a lattice in the presence of broken time-reversal symmetry. This thesis explores the link between FCI states and the quantum Hall effect of the continuum in the context of the Hofstadter model, using a combination of nonperturbative, perturbative and numerical methods. We draw links to experimental realisations of topological phases, and go on to consider a novel way of generating general FCI states using strong interactions on a lattice. We begin by considering the Hofstadter model at weak field, where we use a semiclassical analysis to obtain nonperturbative expressions for the band structure and Berry curvature of the single-particle eigenstates. We use this calculation to justify a perturbative approximation, an approach that we extend to the case when the amount of flux per plaquette is close to a rational fraction with a small denominator. We find that eigenstates of the system are single- or multicomponent wavefunctions that connect smoothly to the Landau levels of the continuum. The perturbative corrections to these are higher Landau level contributions that break rotational invariance and allow the perturbed states to adopt the symmetry of the lattice. In the presence of interactions, this approach allows for the calculation of generalised Haldane pseudopotentials, and in turn, the many-body properties of the system. The method is sufficiently general that it can apply to a wide variety of lattices, interactions, and magnetic field strengths. We present numerical simulations of the Hofstadter model relevant to its recent experimental realisation using optical lattices, noting the additional complications that arise in the presence of an external trap. Finally, we show that even if a noninteracting system is topologically trivial, it is possible to stabilise an FCI state by introducing strong interactions that break time-reversal symmetry. We show that this method may also be used to create a (time-reversal symmetric) fractional topological insulator, and provide numerical evidence to support our argument.

In this thesis we study three examples of interacting many-body systems undergoing a non equilibrium time evolution. Firstly we consider the time evolution in an integrable system: the sine-Gordon field theory in the repulsive regime. We will focus on the one point function of the semi-local vertex operator eiβφ(x)/2 on a specific class of initial states. By analytical means we show that the expectation value considered decays exponentially to zero at late times and we determine the decay time. The method employed is based on a form-factor expansion and uses the "Representative Eigenstate Approach" of Ref. [73] (a.k.a. "Quench Action"). In a second example we study the time evolution in models close to "special" integrable points characterised by hidden symmetries generating infinitely many local conservation laws that do not commute with one another, in addition to the infinite commuting family implied by integrability. We observe that both in the case where the perturbation breaks the integrability and when it breaks only the additional symmetries maintaining integrability, the local observables show a crossover behaviour from an initial to a final quasi stationary plateau. We investigate a weak coupling limit, identify a time window in which the effects of the perturbations become significant and solve the time evolution through a mean-field mapping. As an explicit example we study the XYZ spin-1/2 chain with additional perturbations that break integrability. Finally, we study the effects of integrability breaking perturbations on the non-equilibrium evolution of more general many-particle quantum systems, where the unperturbed integrable model is generic. We focus on a class of spinless fermion models with weak interactions. We employ equation of motion techniques that can be viewed as generalisations of quantum Boltzmann equations. We benchmark our method against time dependent density matrix renormalisation group computations and find it to be very accurate as long as interactions are weak. For small integrability breaking, we observe robust prethermalisation plateaux for local observables on all accessible time scales. Increasing the strength of the integrability breaking term induces a "drift" away from the prethermalisation plateaux towards thermal behaviour. We identify a time scale characterising this crossover.

In the first part of this thesis, we discuss some aspects of the four-dimensional N = 2 superconformal index of theories of class S. We first consider a generalized index on S1 × S3/Zr, and prove S-duality in a particular fugacity slice. We then go on to study the (round) superconformal index in the presence of surface defects. We develop a systematic prescription to compute surface defects labeled by arbitrary irreducible representations of the gauge group and subject those defects to various tests in several different limits. Each of these limits is interesting in its own right, and we go on to explore them in some depth. In the second part of this thesis, we construct the gravity duals of large N supersymmetric gauge theories defined on squashed five-spheres with SU(3) × U(1) symmetry. The gravity duals are constructed in Euclidean Romans F(4) gauged supergravity in six- dimensions, and uplift to massive type IIA supergravity. We compute the partition function and Wilson loop in the large N limit of the gauge theory and compare them to their corresponding supergravity dual quantities. As expected from AdS/CFT, both sides agree perfectly. Based on these results, we conjecture a general formula for the partition function and Wilson loop on any five-sphere background, which for fixed gauge theory depends only on a certain supersymmetric Killing vector. We then go on to construct rigid supersymmetric gauge theories on more general Riemannian five-manifolds. We follow a holographic approach, realizing the manifold as the conformal boundary of the six-dimensional bulk supergravity solution. This leads to a systematic classification of five-dimensional supersymmetric backgrounds with gravity duals.

Phase lies at the heart of quantum physics and quantum information theory. A quantum bit is qualitatively different from a classical bit as it allows for the coherent superposition of possibilities, which demonstrate different behaviours depending on the phase between them. These behaviours constitute as interference phenomena, and lie behind the existence of algorithms in quantum computing which are arguably faster than the best classical alternatives. The concept of phase is deeply steeped in the structure of Hilbert spaces: the mathematical framework that underlies quantum theory. What if quantum theory did not hold in all scenarios, or was only a limiting case of some broader theory? In this case, would we still be able to meaningfully talk about phase and interference? In this thesis, we will adopt an operational generalisation of quantum theory known as the framework of generalised probabilistic theories. We will provide a reasonable definition of phase in this framework. Using this, we shall explore single-particle interferometry set-ups (particularly Mach-Zehnder interferometers): experiments whose output is highly dependent on the phase between the spatially disjoint branches through which a particle might be traversing. By applying physically-motivated locality considerations, we identify the crucial role that the uncertainty principle and its generalisations play in quantum theory as an enabler of non-trivial interference. By taking into account relativity of simultaneity, we will also provide a physical motivation for why standard quantum theory provides the best description of the location of a particle traversing such a system. Finally, we apply our generalised definition of phase in the related context of particle exchange behaviour, and identify a method for classifying post-quantum particles. All of this will demonstrate that phase between possibilities and its consequences are not uniquely quantum phenomena. Much of the behaviour we might ascribe to phase in quantum theory in fact holds generally true for phase in probabilistic theories.

Molecular biophysics is a rapidly evolving field aimed at the physics-based investigation of the biomolecular processes that enable life. In this thesis, we explore two such processes: the thermodynamics of DNA bending, and the mechanism of the RecQ DNA helicase. A computational approach using a coarse-grained model of DNA is employed for the former; an experimental approach relying heavily on single-molecule fluorescence for the latter. There is much interest in understanding the physics of DNA bending, due to both its biological role in genome regulation and its relevance to nanotechnology. Small DNA bending fluctuations are well described by existing models; however, there is less consensus on what happens at larger bending fluctuations. A coarse-grained simulation is used to fully characterize the thermodynamics and mechanics of duplex DNA bending. We then use this newfound insight to harmonize experimental results between four distinct experimental systems: a 'molecular vise', DNA cyclization, DNA minicircles and a 'strained duplex'. We find that a specific structural defect present at large bending fluctuations, a 'kink', is responsible for the deviation from existing theory at lengths below about 80 base pairs. The RecQ DNA helicase is also of much biological and clinical interest, owing to its essential role in genome integrity via replication, recombination and repair. In humans, heritable defects in the RecQ helicases manifest clinically as premature aging and a greatly elevated cancer risk, in disorders such as Werner and Bloom syndromes. Unfortunately, the mechanism by which the RecQ helicase processes DNA remains poorly understood. Although several models have been proposed to describe the mechanics of helicases based on biochemical and structural data, ensemble experiments have been unable to address some of the more nuanced questions of helicase function. We prepare novel substrates to probe the mechanism of the RecQ helicase via single-molecule fluorescence, exploring DNA binding, translocation and unwinding. Using this insight, we propose a model for RecQ helicase activity.

In this Thesis I explore aspects of dark radiation and its role in String Phenomenology. Dark radiation is any additional hidden type of relativistic matter present in the Universe today, conventionally labelled as an "excess effective number of neutrino species", Δ Neff. It provides a powerful test of hitherto untested theoretical models based on fundamental theories such as String Theory. I begin by considering dark radiation in the LARGE Volume Scenario, a phenomenologically viable class of string compactifications. First I review how the minimal setup slightly overproduces axionic dark radiation via modulus decay. I then demonstrate that loop corrections to the main competing visible-sector decay process have a negligible effect and are unable to alleviate the tension with observations. In the following chapter I explore fibred extensions of the LARGE Volume Scenario. The predictions for Δ Neff are qualitatively different: in particular, models with a sequestered visible sector on D3 branes at a singularity are swamped by massless axions and decisively ruled out. I then consider TeV-scale supersymmetry in a model with anisotropic modulus stabilisation. If the Standard Model is realised on D7 branes wrapping the small volume cycle a hierarchy of soft terms is generated, which may have applications to natural supersymmetry. The final chapter takes a different approach and investigates the proposition that dark radiation, in the form of a Cosmic Axion Background, could explain the long-standing soft X-ray excess from galaxy clusters. I show for the Coma cluster that the morphology of the excess can be reproduced by axion-photon conversion in the intracluster magnetic field, provided the field is allowed to have more structure on smaller scales than typically assumed based on Faraday rotation data. This explanation requires an inverse axion-photon coupling M ∼ 1011 - 1012 GeV and a mean axion energy (ECAB) ∼ 50 - 250 eV.

This thesis considers quantum impurity models that exhibit a quantum phase transition (QPT) between a Fermi liquid strong coupling (SC) phase, and a doubly-degenerate non-Fermi liquid local moment (LM) phase. We focus on what can be said from exact analytic arguments about the LM phase of these models, where the system is characterized by an SU(2) spin degree of freedom in the entire system. Conventional perturbation theory about the non-interacting limit does not hold in the non-Fermi liquid LM phase. We circumvent this problem by reformulating the perturbation theory using a so-called `two self-energy' (TSE) description, where the two self-energies may be expressed as functional derivatives of the Luttinger-Ward functional. One particular paradigmatic model that possesses a QPT between SC and LM phases is the pseudogap Anderson impurity model (PAIM). We use infinite-order perturbation theory in the interaction, U, to self-consistently deduce the exact low-energy forms of both the self-energies and propagators in each of the distinct phases of the model. We analyse the behaviour of the model approaching the QPT from each phase, focusing on the scaling of the zero-field single-particle dynamics using both analytical arguments and detailed numerical renormalization group (NRG) calculations. We also apply two `conserving' approximations to the PAIM. First, second-order self-consistent perturbation theory and second, the fluctuation exchange approximation (FLEX). Within the FLEX approximation we develop a numerical algorithm capable of self-consistently and coherently describing the QPT coming from both distinct phases. Finally, we consider a range of static spin susceptibilities that each probe the underlying QPT in response to coupling to a magnetic field.

We calculate the string tensions, mass spectrum, and deconfining temperatures of SO(N) gauge theories in 2+1 dimensions. After a review of lattice field theory, we describe how we simulate the corresponding lattice gauge theories, construct operators to project on to specific states, and extrapolate values to the continuum limit. We discuss how to avoid possible complications such as finite size corrections and the bulk transition. SO(N) gauge theories have become recently topical since they do not have a fermion sign problem, are orbifold equivalent to SU(N) gauge theories, and share a common large-N limit in their common sector of states with SU(N) gauge theories. This motivates us to compare the physical properties of SO(N) and SU(N) gauge theories between 'group equivalences', which includes Lie algebra equivalences such as SO(6) and SU(4), and particularly a large-N equivalence. We discuss the large-N orbifold equivalence between SO(N) and SU(N) gauge theories, which relates the large-N gauge theories perturbatively. Using large-N extrapolations at fixed 't Hooft coupling, we test to see if SO(N) gauge theories and SU(N) gauge theories share non-perturbative properties at the large-N limit. If these group equivalences lead to similar physics in the gauge theories, then we could imagine doing finite chemical potential calculations that are currently intractable in SU(N) gauge theories by calculating equivalent quantities in the corresponding SO(N) gauge theories. We show that the SO(N) and SU(N) values match between group equivalences and at the large-N limit.

Hydrodynamics is an effective theory that is extremely successful in describing a wide range of physical phenomena in liquids, gases and plasmas. However, our understanding of the structure of the theory, its microscopic origins and its behaviour at strong coupling is far from complete. To understand how an effective theory of dissipative hydrodynamics could emerge from a closed microscopic system, we analyse the structure of effective Schwinger-Keldysh Closed-Time-Path theories. We use this structure and the action principle for open systems to derive the energy-momentum balance equation for a dissipative fluid from an effective CTP Goldstone action. Near hydrodynamical equilibrium, we construct the first-order dissipative stress-energy tensor and derive the Navier-Stokes equations. Shear viscosity is shown to vanish, while bulk viscosity and thermodynamical quantities are determined by the form of the effective action. The exploration of strongly interacting states of matter, particularly in the hydrodynamic regime, has been a major recent application of gauge/string duality. The strongly coupled theories involved are typically deformations of large-$N$ SUSY gauge theories with exotic matter that are unusual from a low-energy point of view. In order to better interpret holographic results, an understanding of the weak-coupling behaviour of such gauge theories is essential. We study the exact and SUSY-broken N=1 and N=2 super-QED with finite densities of electron number and R-charge, respectively. Despite the fact that fermionic fields couple to the chemical potentials, the strength of scalar-fermion interactions, fixed by SUSY, prevents a Fermi surface from forming. This is important for hydrodynamical excitations such as zero sound. Intriguingly, in the absence of a Fermi surface, the total charge need not be stored in the scalar condensates alone and fermions may contribute. Gauss-Bonnet gravity is a useful laboratory for non-perturbative studies of the higher derivative curvature effects on transport coefficients of conformal fluids with holographic duals. It was previously known that shear viscosity can be tuned to zero by adjusting the Gauss-Bonnet coupling, λGB, to its maximal critical value. To understand the behaviour of the fluid in this limit, we compute the second-order transport coefficients non-perturbatively in λGB and show that the fluid still produces entropy, while diffusion and sound attenuation are suppressed at all order in the hydrodynamic expansion. We also show that the theory violates a previously proposed universal relation between three of the second order transport coefficients. We further compute the only second-order coefficient thus far unknown, λ2, in the N=4 super Yang-Mills theory with the leading-order 't Hooft coupling correction. Intriguingly, the universal relation is not violated by these leading-order perturbative corrections. Finally, by adding higher-derivative photon field terms to the action, we study charge diffusion and non-perturbative parameter regimes in which the charge diffusion constant vanishes.

In this thesis I discuss the nature of ‘measurement’ in quantum theory. ‘Measurement’ is associated with several different processes: the gradual imprinting of information about one system onto another, which is well understood; the collapse of the wavefunction, which is ill-defined and troublesome; and finally, the means by which inferences about unknown experimental parameters are made. I present a theoretical extension to an experimental proposal from Leggett and Garg, who suggested that the quantum-or-classical reality of a macroscopic system may be probed with successive measurements arrayed in time. The extension allows for a finite level of imperfection in the protocol, and makes use of Leggett’s ‘null result’ measurement scheme. I present the results of an experiment conducted in Oxford that, up to certain loopholes, defies a non-quantum interpretation of the dynamics of phosphorous nuclei embedded in silicon. I also present the theory of statistical parameter estimation, and discover that a recent trend to employ time symmetric ‘postselected’ measurements offers no true advantage over standard methods. The technique, known as weak-value amplification, combines a weak transfer of quantum information from system to meter with conditional data rejection, to surprising effect. The Fisher information is a powerful tool for evaluating the performance of any parameter estimation model, and it reveals the technique to be worse than ordinary, preselected only measurements. That this is true despite the presence of noise (including magnetic field fluctuations causing deco- herence, poor resolution detection, and random displacements), casts serious doubt on the utility of the method.

This thesis is concerned with modelling the dynamics of open quantum systems in several different contexts. Of principal interest is the manner in which the environment can modify, or even dominate, a system’s quantum behaviour in order to facilitate the transport of energetic excitations. In the first research chapter, a time-local, non-Markovian quantum master equation is derived in a variationally defined reference frame, for networks of two-level systems coupled to bosonic environments. The predictions of this master equation are then compared with those derived using both weak-coupling and polaron approximations. The variational master equation is found to agree with these standard approaches in their regimes of validity, whilst interpolating between them in intermediate parameter regimes. The second research chapter focusses on the dynamics of a superconducting double quantum dot embedded in a resonant circuit. The device is considered in a regime where the ground state consists of a coherent spatial superposition of a single Cooper pair, which can be excited by a variety of interactions with the environment. The relevant transition rates are calculated and the processes responsible are identified. A numerical simulation of the system is then used to explain experimental data, and show that for certain parameters a significant fraction of excitations occur via absorption of photons from the environment. The final chapter considers a model for an olfactory receptor, in which odorant molecules are recognised by their vibrational modes. Electron transfer occurs in the receptor, dependent on the presence of a vibrational mode of the right frequency. A quantum master equation for the system is derived, and the resulting dynamics is compared to earlier semi-classical treatments. The behaviour of the receptor is found to be sensitive not only to the frequency of the vibrational mode, but also to the character of the surrounding environment. Increased dissipation on the odorant mode, as well as the presence of higher frequencies in the environment is found to improve the frequency resolution of the receptor.

The lack of direct evidence for physics beyond the SM at the LHC has led some to reevaluate the need for such physics to solve the hierarchy problem. Instead, the notion that the SM, or something like it, is valid up to the Planck scale and that technical naturalness is sufficient for solving the hierarchy problem has been suggested. This thesis examines minimal extensions of the SM that address its phenomenological and theoretical shortcomings while avoiding new physics between the electroweak and Planck scales that introduces a hierarchy problem. This thesis first studies two issues with the vMSM - an extension of the SM by three right-handed neutrinos - and their possible solutions. The first issue is the tension between dark matter production in the nuMSM and constraints from the Lyman-alpha forest data. To avoid this tension, the vMSM is extended by a Higgs singlet Φ and neutrino dark matter is produced through the decays of Φ rather than through left-right neutrino mixing. It is shown that the hierarchical parameters of this model can arise from symmetries broken at or near the Planck scale for two specific examples: one in which Φ stabilizes the electroweak vacuum and one in which Φ is a light inflaton. The second issue pertains to Higgs ξ-inflation. In the vMSM, a large non-minimal coupling ξ of the Higgs to gravity gives inflation but leads to a possible violation of perturbative unitarity below the inflationary scale. A study of Higgs ξ-inflation with Mh ≃ 125-126 GeV, for which the Higgs self-coupling λ runs to small values near the Planck scale, is carried out. It is shown that small λ can significantly reduce ξ required for inflation, but ξ cannot be small enough to address the possible unitarity issue. For small λ, a new region of Higgs ξ-inflation with a large tensor-to-scalar ratio r that is consistent with BICEP2 is discovered. This thesis then studies the technical naturalness and cosmology of a model that addresses the strong CP problem. It is shown that a classically scale invariant DFSZ invisible aξon model with a Peccei-Quinn scalar S, whose couplings to the SM are ultra-weak, can solve the strong CP problem and generate electroweak symmetry breaking via the Coleman-Weinberg mechanism. The ultra-weak couplings of S are natural due to an underlying approξmate shift symmetry. The model contains a light pseudo-Goldstone dilaton that can be consistent with cosmological bounds while the aξon can be the dark matter of the universe. Finally, a summary of the thesis is presented and future research topics are suggested.

The striking evidence for the existence of dark matter in the Universe implies that there is new physics to be discovered beyond the Standard Model. To identify the nature of this dark matter is a key task for modern astroparticle physics, and a large number of experiments pursuing a range of different search strategies have been developed to solve it. The topic of this thesis is the complementarity of these different experiments and the issue of how to combine the information from different searches independently of experimental and theoretical uncertainties. The first part focuses on the direct detection of dark matter scattering in nuclear recoil detectors, with a special emphasis on the impact of the assumed velocity distribution of Galactic dark matter particles. By converting experimental data to variables that make the astrophysical unknowns explicit, different experiments can be compared without implicit assumptions concerning the dark matter halo. We extend this framework to include annual modulation signals and apply it to recent experimental hints for dark matter, showing that the tension between these results and constraints from other experiments is independent of astrophysical uncertainties. We explore possible ways of ameliorating this tension by changing our assumptions on the properties of dark matter interactions. In this context, we propose a new approach for inferring the properties of the dark matter particle, which does not require any assumptions about the structure of the dark matter halo. A particularly interesting option is to study dark matter particles that couple differently to protons and neutrons (so-called isospin-violating dark matter). Such isospin-violation arises naturally in models where the vector mediator is the gauge boson of a new U(1) that mixes with the Standard Model gauge bosons. In the second part, we first discuss the case where both the Z' and the dark matter particle have a mass of a few GeV and then turn to the case where the Z' is significantly heavier. While the former case is most strongly constrained by precision measurements from LEP and B-factories, the latter scenario can be probed with great sensitivity at the LHC using monojet and monophoton searches, as well as searches for resonances in dijet, dilepton and diboson final states. Finally, we study models of dark matter where loop contributions are important for a comparison of LHC searches and direct detection experiments. This is the case for dark matter interactions with Yukawa-like couplings to quarks and for interactions that lead to spin-dependent or momentum suppressed scattering cross sections at tree level. We find that including the contribution from heavy-quark loops can significantly alter the conclusions obtained from a tree-level analysis.

This thesis contains a study of topological phases of matter, with a strong emphasis on symmetry as a unifying theme. We take the point of view that the "topology" in many examples of what is loosely termed "topological matter", has its origin in the symmetry data of the system in question. From the fundamental work of Wigner, we know that topology resides not only in the group of symmetries, but also in the cohomological data of projective unitary-antiunitary representations. Furthermore, recent ideas from condensed matter physics highlight the fundamental role of charge-conjugation symmetry. With these as physical motivation, we propose to study the topological features of gapped phases of free fermions through a Z2-graded C*-algebra encoding the symmetry data of their dynamics. In particular, each combination of time reversal and charge conjugation symmetries can be associated with a Clifford algebra. K-theory is intimately related to topology, representation theory, Clifford algebras, and Z2-gradings, so it presents itself as a powerful tool for studying gapped topological phases. Our basic strategy is to use various K