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In general relativity, the allowed set of diffeomorphisms or gauge transformations at asymptotic infinity forms the BMS group, an infinite-dimensional extension of the Poincaré group. We focus on the structure of the BMS group in two distinct forms of Hamiltonian dynamics — the instant and front forms. Both similarities and differences in these two forms are examined while emphasizing the role of noncovariant approaches to symmetries in gravity. [ABSTRACT FROM AUTHOR]

We introduce a new symmetry, light-cone reflection (LCR), which interchanges timelike and spacelike intervals. Our motivation is to provide a reason, based on symmetry, why tachyons might exist, with emphasis on application to neutrinos. We show that LCR, combined with translations, leads to a much larger symmetry. We construct an LCR-invariant Lagrangian and discuss some of its properties. In a simple example, we find complete symmetry in the spectrum between tachyons and ordinary particles. We also show that the theory allows for the introduction of a further gauge invariance related to chiral symmetry. [ABSTRACT FROM AUTHOR]

There has been a surge of interest in effective non-Lorentzian theories of excitations with restricted mobility, known as fractons. Examples include defects in elastic materials, vortex lattices or spin liquids. In the effective theory novel coordinate-dependent symmetries emerge that shape the properties of fractons. In this review we will discuss these symmetries, cover the effective description of gapless fractons via elastic duality, and discuss their hydrodynamics.

In this paper, we have adopted a new approach to study the Killing vector fields of locally rotationally symmetric and general Bianchi type I spacetimes. Instead of directly integrating the set of Killing's equations, an algorithm is developed in Maple which converts these equations to the reduced involutive form (Rif) and consequently it imposes some restrictions on the metric functions in the form of a tree, known as Rif tree. The set of Killing's equations is then solved for each branch of the Rif tree, giving the explicit form of the Killing vector fields. The structure of Lie algebra is presented for each set of the obtained Killing vector fields and some physical implications of the obtained metrics are discussed. [ABSTRACT FROM AUTHOR]

We introduce a new symmetry, light-cone reflection (LCR), which interchanges timelike and spacelike intervals. Our motivation is to provide a reason, based on symmetry, why tachyons might exist, with emphasis on application to neutrinos. We show that LCR, combined with translations, leads to a much larger symmetry. We construct an LCR-invariant Lagrangian and discuss some of its properties. In a simple example, we find complete symmetry in the spectrum between tachyons and ordinary particles. We also show that the theory allows for the introduction of a further gauge invariance related to chiral symmetry.

Conditions are found which ensure that local boost invariance (LBI), invariance under a linear boost isotropy, implies local boost symmetry (LBS), i.e. the existence of a local group of motions such that for every point P in a neighbourhood there is a boost leaving P fixed. It is shown that for Petrov type D spacetimes this requires LBI of the Riemann tensor and its first derivative. That is also true for most conformally flat spacetimes, but those with Ricci tensors of Segre type [1(11,1)] may require LBI of the first three derivatives of curvature to ensure LBS. [ABSTRACT FROM AUTHOR]

Abstract We analyze non-linear interactions of 2N -form Maxwell fields in a space-time of dimension D = 4N.Based on the Pasti-Sorokin-Tonin (PST) method, we derive the general consistency condition for the dynamics to respect both manifest SO(2)-duality invariance and manifest Lorentz invariance. For a generic dimension D = 4N, we determine a canonical class of exact solutions of this condition, which represent a generalization of the known non-linear duality invariant Maxwell theories in D = 4. The resulting theories are shown to be equivalent to a corresponding class of canonical theories formulated à la Gaillard-Zumino-Gibbons-Rasheed (GZGR), where duality is a symmetry only of the equations of motion. In dimension D = 8, via a complete solution of the PST consistency condition, we derive new non-canonical manifestly duality invariant quartic interactions. Correspondingly, we construct new non-trivial quartic interactions also in the GZGR approach, and establish their equivalence with the former. In the presence of charged dyonic p-brane sources, we reveal a basic physical inequivalence of the two approaches. The power of our method resides in its universal character, reducing the construction of non-linear duality invariant Maxwell theories to a purely algebraic problem.

Abstract We study string theory on the pp-wave geometry obtained by taking the Penrose limit around a certain null geodesic of the non-supersymmetric Schrödinger background. We solve for the spectrum of bosonic excitations and find compelling agreement with the dispersion relation of the giant magnons in the Schrödinger background obtained previously in [47]. Inspired by the pp-wave spectrum we conjecture an exact in the t’Hooft coupling dispersion relation for the magnons in the original Schrödinger background. We show that the pp-wave background admits exactly 16 Killing spinors. We use the explicit form of the latter in order to derive the supersymmetry algebra of the background which explicitly depends on the deformation parameter. Its bosonic subalgebra is of the Newton-Hooke type.

Abstract In this work we study the Sorkin-Johnston (SJ) vacuum in de Sitter spacetime for free scalar field theory. For the massless theory we find that the SJ vacuum can neither be obtained from the O(4) Fock vacuum of Allen and Folacci nor from the non-Fock de Sitter invariant vacuum of Kirsten and Garriga. Using a causal set discretisation of a slab of 2d and 4d de Sitter spacetime, we find the causal set SJ vacuum for a range of masses m ≥ 0 of the free scalar field. While our simulations are limited to a finite volume slab of global de Sitter spacetime, they show good convergence as the volume is increased. We find that the 4d causal set SJ vacuum shows a significant departure from the continuum Mottola-Allen α-vacua. Moreover, the causal set SJ vacuum is well-defined for both the minimally coupled massless m = 0 and the conformally coupled massless m = m c cases. This is at odds with earlier work on the continuum de Sitter SJ vacuum where it was argued that the continuum SJ vacuum is ill-defined for these masses. Our results hint at an important tension between the discrete and continuum behaviour of the SJ vacuum in de Sitter and suggest that the former cannot in general be identified with the Mottola-Allen α-vacua even for m > 0.

Abstract We show that the BMS-supertranslations and their associated supermomenta on past null infinity can be related to those on future null infinity, proving the conjecture of Strominger for a class of spacetimes which are asymptotically-flat in the sense of Ashtekar and Hansen. Using a cylindrical 3-manifold of both null and spatial directions of approach towards spatial infinity, we impose appropriate regularity conditions on the Weyl tensor near spatial infinity along null directions. The asymptotic Einstein equations on this 3-manifold and the regularity conditions imply that the relevant Weyl tensor components on past null infinity are antipodally matched to those on future null infinity. The subalgebra of totally fluxless supertranslations near spatial infinity provides a natural isomorphism between the BMS-supertranslations on past and future null infinity. This proves that the flux of the supermomenta is conserved from past to future null infinity in a classical gravitational scattering process provided additional suitable conditions are satisfied at the timelike infinities.

Abstract We calculate the constitutive equations of the stress-energy tensor and the currents of the free massless Dirac field at thermodynamic equilibrium with acceleration and rotation and a conserved axial charge by using the density operator approach. We carry out an expansion in thermal vorticity to the second order with finite axial chemical potential μ A . The obtained coefficients of the expansion are expressed as correlators of angular momenta and boost operators with the currents. We confirm previous observations that the axial chemical potential induces non-vanishing components of the stress-energy tensor at first order in thermal vorticity due to breaking of parity invariance of the density operator with μ A ≠ 0. The appearance of these components might play an important role in chiral hydrodynamics.

Abstract We study a toy model of the Kerr/CFT correspondence using string theory on AdS3 × S 3. We propose a single trace irrelevant deformation of the dual CFT generated by a vertex operator with spacetime dimensions (2, 1). This operator shares the same quantum numbers as the integrable T J ¯ $$ T\overline{J} $$ deformation of two-dimensional CFTs where J ¯ $$ \overline{J} $$ is a chiral U(1) current. We show that the deformation is marginal on the worldsheet and that the target spacetime is deformed to null warped AdS3 upon dimensional reduction. We also calculate the spectrum of the deformed theory on the cylinder and compare it to the field theory analysis of T J ¯ $$ T\overline{J} $$ -deformed CFTs.

Abstract In order to deal with IR divergences arising in QED or perturbative quantum gravity scattering processes, one can either calculate inclusive quantities or use dressed asymptotic states. We consider incoming superpositions of momentum eigenstates and show that in calculations of cross-sections these two approaches yield different answers: in the inclusive formalism no interference occurs for incoming finite superpositions and wavepackets do not scatter at all, while the dressed formalism yields the expected interference terms. This suggests that rather than Fock space states, one should use Faddeev-Kulish-type dressed states to correctly describe physical processes involving incoming superpositions. We interpret this result in terms of selection rules due to large U(1) gauge symmetries and BMS supertranslations.

Abstract We calculate the one-loop contributions to the polarization operator for scalar quantum electrodynamics in different external electromagnetic and gravitational fields. In the case of gravity, de Sitter space and its different patches were considered. It is shown that the Debye mass appears only in the case of alpha-vacuum in the Expanding Poincare Patch. It can be shown either by direct computations or by using analytical and causal properties of the de Sitter space. Also, the case of constant electric field is considered and the Debye mass is calculated.

Abstract We show how twisting the spectral triple of the Standard Model of elementary particles naturally yields the Krein space associated with the Lorentzian signature of spacetime. We discuss the associated spectral action, both for fermions and bosons. What emerges is a tight link between twists and Wick rotation.

The question about the relation between spacetime structure and the symmetries of laws has received renewed attention in a recent discussion about the status of Minkowski spacetime in Special Relativity. In that context we find two extreme positions (either spacetime explains symmetries of laws or vice-versa) and a general assumption about the debate being mainly about explanation. The aim of this paper is twofold: first, to argue that the ontological dimension of the debate cannot be ignored; second, to claim that taking ontology into account involves considering a third perspective on the relation between spacetime and symmetries of laws; one in which both terms would be somehow derived from common assumptions on the formulation of a given physical theory. [ABSTRACT FROM AUTHOR]

The Dirac equation with chiral symmetry is derived using the irreducible representations of the Poincaré group, the Lagrangian formalism, and a novel method of projection operators that takes as its starting point the minimal assumption of four linearly independent physical states. We thereby demonstrate the fundamental nature of this form of the Dirac equation. The resulting equation is then examined within the context of spacetime and CPT symmetries with a discussion of the implications for the general formulation of physical theories.

Abstract It is shown that the notion of Conformal Mass can be defined within a given anti-de Sitter (AdS) branch of a Lovelock gravity theory as long as the corresponding vacuum is not degenerate. Indeed, conserved charges obtained by the addition of Kounterterms to the bulk action turn out to be proportional to the electric part of the Weyl tensor, when the fall-off of a generic solution in that AdS branch is considered. The factor of proportionality is the degeneracy condition for the vacua in the particular Lovelock AdS theory under study. This last feature explains the obstruction to define Conformal Mass in the degenerate case.

We review recent theoretical progress and observational constraints on multifractional spacetimes, geometries that change with the probed scale. On the theoretical side, the basic structure of the Standard Model and of the gravitational action is discussed. On the experimental side, we recall the bounds on the scales of the geometry coming from particle physics, astrophysics and the cosmic microwave background. [ABSTRACT FROM AUTHOR]

Gravity can be formulated as a gauge theory by combining symmetry principles and geometrical methods in a consistent mathematical framework. The gauge approach to gravity leads directly to non-Euclidean, post-Riemannian spacetime geometries, providing the adequate formalism for metric-affine theories of gravity with curvature, torsion and non-metricity. In this paper, we analyze the structure of gauge theories of gravity and consider the relation between fundamental geometrical objects and symmetry principles as well as different spacetime paradigms. Special attention is given to Poincaré gauge theories of gravity, their field equations and Noether conserved currents, which are the sources of gravity. We then discuss several topics of the gauge approach to gravitational phenomena, namely, quadratic Poincaré gauge models, the Einstein-Cartan-Sciama-Kibble theory, the teleparallel equivalent of general relativity, quadratic metric-affine Lagrangians, non-Lorentzian connections, and the breaking of Lorentz invariance in the presence of non-metricity. We also highlight the probing of post-Riemannian geometries with test matter. Finally, we briefly discuss some perspectives regarding the role of both geometrical methods and symmetry principles towards unified field theories and a new spacetime paradigm, motivated from the gauge approach to gravity.

Guided by ordinary quantum mechanics we introduce new fuzzy spheres S Λ d of dimensions d = 1 , 2 : we consider an ordinary quantum particle in D = d + 1 dimensions subject to a rotation invariant potential well V ( r ) with a very sharp minimum on a sphere of unit radius. Imposing a sufficiently low energy cutoff to ‘freeze’ the radial excitations makes only a finite-dimensional Hilbert subspace accessible and on it the coordinates noncommutative à la Snyder ; in fact, on it they generate the whole algebra of observables. The construction is equivariant not only under rotations – as Madore’s fuzzy sphere – , but under the full orthogonal group O ( D ) . Making the cutoff and the depth of the well dependent on (and diverging with) a natural number Λ , and keeping the leading terms in 1 ∕ Λ , we obtain a sequence S Λ d of fuzzy spheres converging to the sphere S d in the limit Λ → ∞ (whereby we recover ordinary quantum mechanics on S d ). These models may be useful in condensed matter problems where particles are confined on a sphere by an (at least approximately) rotation-invariant potential, beside being suggestive of analogous mechanisms in quantum field theory or quantum geometry. [ABSTRACT FROM AUTHOR]

We investigate the Kerr–Newman–NUT black hole solution obtained from Plebański–Demiański solutions with several assumptions. The origin of the microscopic entropy of this black hole is investigated using the conjectured Kerr/CFT correspondence which is originally proposed for extremal Kerr black holes. The isometry of the near-horizon extremal Kerr–Newman–NUT black hole shows that the asymptotic symmetry group may be implemented to compute the central charge of the Virasoro algebra. Furthermore, by assuming the Frolov–Thorne vacuum, the conformal temperatures can be obtained. Then by using the Cardy formula, the microscopic entropy is gained which matches the Bekenstein–Hawking entropy. We also employ the Cardy prescription to find the logarithmic correction of the entropy. Then at limit a → 0 , the extremal Reissner–Nordström–NUT solution is recovered and by enhancing with the fibered coordinate we find the five-dimensional (5D) solution. The second dual CFT is applied to this black hole to gain the entropy. Finally, the microscopic entropy is still in agreement with the area law of 5D black hole solution. Hence, the extremal Reissner–Nordström–NUT solution is holographically dual to the CFT. [ABSTRACT FROM AUTHOR]

The gravity model developed in the series of papers (Arbuzov et al. 2009; 2010), (Pervushin et al. 2012) is revisited. The model is based on the Ogievetsky theorem, which specifies the structure of the general coordinate transformation group. The theorem is implemented in the context of the Noether theorem with the use of the nonlinear representation technique. The canonical quantization is performed with the use of reparametrization-invariant time and Arnowitt– Deser–Misner foliation techniques. Basic quantum features of the models are discussed. Mistakes appearing in the previous papers are corrected.

In this paper, we present a complete classification of Bianchi type II spacetime according to Ricci inheritance collineations (RICs). The RICs are classified considering cases when the Ricci tensor is both degenerate as well as non-degenerate. In case of non-degenerate Ricci tensor, it is found that Bianchi type II spacetime admits 4-, 5-, 6- or 7-dimensional Lie algebra of RICs. In the case when the Ricci tensor is degenerate, majority cases give rise to infinitely many RICs, while remaining cases admit finite RICs given by 4, 5 or 6. [ABSTRACT FROM AUTHOR]

In theories of the Kaluza-Klein kind there are spins or total angular moments in higher dimensions which manifest as charges in the observable d = (3 + 1). The charge conjugation requirement, if following the prescription in (3 + 1), would transform any particle state out of the Dirac sea into the hole in the Dirac sea, which manifests as an anti-particle having all the spin degrees of freedom in d, except S, the same as the corresponding particle state. This is in contradiction with what we observe for the anti-particle. In this paper we redefine the discrete symmetries so that we stay within the subgroups of the starting group of symmetries, while we require that the angular moments in higher dimensions manifest as charges in d = (3 + 1). We pay attention on spaces with even d. [ABSTRACT FROM AUTHOR]

We provide a careful development and rigorous proof of the CPT theorem within the framework of mainstream (Lagrangian) quantum field theory. This is in contrast to the usual rigorous proofs in purely axiomatic frameworks, and non-rigorous proof-sketches in the mainstream approach. We construct the CPT transformation for a general field directly, without appealing to the enumerative classification of representations, and in a manner that is clearly related to the requirements of our proof. Our approach applies equally in Minkowski spacetimes of any dimension at least three, and is in principle neutral between classical and quantum field theories: the quantum CPT theorem has a natural classical analogue. The key mathematical tool is that of complexification; this tool is central to the existing axiomatic proofs, but plays no overt role in the usual mainstream approaches to CPT. [ABSTRACT FROM AUTHOR]