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Relativistic, charged, superheated bubbles may play an important role in neutron star mergers if first-order phase transitions are present in the phase diagram of Quantum Chromodynamics. We describe the properties of these bubbles in the hydrodynamic regime. We find two qualitative differences with supercooled bubbles. First, the pressure inside an expanding superheated bubble can be higher or lower than the pressure outside the bubble. Second, some fluid flows develop metastable regions behind the bubble wall. We consider the possible role of a conserved charge akin to baryon number. The fluid flow profiles are unaffected by this charge if the speed of sound is constant in each phase, but they are modified for more general equations of state. We compute the efficiency factor relevant for gravitational wave production., Comment: 18 pages, 8 figures, 1 appendix

Holography relates gravitational theories in five dimensions to four-dimensional quantum field theories in flat space. Under this map, the equation of state of the field theory is encoded in the black hole solutions of the gravitational theory. Solving the five-dimensional Einstein's equations to determine the equation of state is an algorithmic, direct problem. Determining the gravitational theory that gives rise to a prescribed equation of state is a much more challenging, inverse problem. We present a novel approach to solve this problem based on physics-informed neural networks. The resulting algorithm is not only data-driven but also informed by the physics of the Einstein's equations. We successfully apply it to theories with crossovers, first- and second-order phase transitions.

Plasmonic nanoantennas, metallodielectric structures with engineered size and shape, have attracted much attention lately as they make the control of the directionality and temporal characteristics of light emitted by fluorophores possible. Nanoantennas exploit light-matter interactions mediated by Localized Surface Plasmon Resonances and, so far, have been demonstrated using metallic nanoparticles or other metallic nanostructures. Plasmonic picocavities, i.e., plasmonic cavities with mode volumes below 1 cubic nanometer, could act as antennas to mediate light-matter interaction even more efficiently than their nanoscale counterparts due to their extreme field confinement, but the directionality on their emission is difficult to control. In this work, we show that the plasmonic picocavity formed between the tip of a Scanning Tunnelling Microscope and a metal surface with a monoatomic step shows directional emission profiles and, thus, can be considered as a realization of a picoantenna. Comparison with electromagnetic calculations demonstrates that the observed directionality arises from light emission tilting of the picocavity plasmons. Our results, thus, pave the way to exploiting picoantennas as an efficient way to control light-matter interaction at the nanoscale.

General Relativity predicts that the spacetime near a cosmological singularity undergoes an infinite number of chaotic oscillations between different Kasner epochs with rapid transitions between them. This so-called BKL behaviour persists in the presence of several types of classical matter. Little is known in the presence of quantum effects. A major obstacle is the fact that the fast metric oscillations inevitably drive the matter far from equilibrium. We use holography to determine the evolution of the quantum stress tensor of a non-conformal, strongly-coupled, four-dimensional gauge theory in a Kasner spacetime. The stress tensor near the singularity is solely controlled by the ultraviolet fixed point of the gauge theory, and it diverges in a universal way common to all theories with a gravity dual. We then compute the backreaction of the stress tensor on the Kasner metric to leading order in the gravitational coupling. The modification of the Kasner exponents that we find suggests that the BKL behaviour may be avoided in the presence of quantum matter., Comment: 6 pages, 4 figures

Neutron star mergers provide a unique laboratory for the study of strong-field gravity coupled to Quantum Chromodynamics in extreme conditions. The frequencies and amplitudes of the resulting gravitational waves encode invaluable information about the merger. Simulations to date have shown that these frequencies lie in the kilo-Hertz range. They have also shown that, if Quantum Chromodynamics possesses a first-order phase transition at high baryon density, then this is likely to be accessed during the merger dynamics. Here we show that this would result in the nucleation of superheated and/or supercompressed bubbles whose subsequent dynamics would produce gravitational waves in the Mega-Hertz range. We estimate the amplitude of this signal and show that it may fall within the expected sensitivity of future superconducting radio-frequency cavity detectors for mergers at distances up to tens of Mega-parsecs., Comment: 11 pages, 4 figures

Cosmological phase transitions can proceed via the nucleation of bubbles that subsequently expand and collide. The resulting gravitational wave spectrum depends crucially on the properties of these bubbles. We extend our previous holographic work on planar bubbles to circular bubbles in a strongly-coupled, non-Abelian, four-dimensional gauge theory. This extension brings about two new physical properties. First, the existence of a critical bubble, which we determine. Second, the bubble profile at late times exhibits a richer self-similar structure, which we verify. These results require a new 3+1 evolution code called Jecco that solves the Einstein equations in the characteristic formulation in asymptotically AdS spaces. Jecco is written in the Julia programming language and is freely available. We present an outline of the code and the tests performed to assess its robustness and performance., Comment: 63 pages, 23 figures. minor typo fixed

We uncover a new gravitational-wave production mechanism in cosmological, first-order, thermal phase transitions. These are usually assumed to proceed via the nucleation of bubbles of the stable phase inside the metastable phase. However, if the nucleation rate is sufficiently suppressed, then the Universe may supercool all the way down the metastable branch and enter the spinodal region. In this case the transition proceeds via the exponential growth of unstable modes and the subsequent formation, merging and relaxation of phase domains. We use holography to follow the real-time evolution of this process in a strongly coupled, four-dimensional gauge theory. The resulting gravitational wave spectrum differs qualitatively from that in transitions mediated by bubble nucleation. We discuss the possibility that the spinodal dynamics may be preceded by a period of thermal inflation., Comment: 45 pages, 19 figures

We use holography to study collisions of phase domains formed in a four-dimensional, strongly-coupled gauge theory with a first-order, thermal phase transition. We find three qualitatively different dynamical regimes depending on the collision velocity. For low velocities the domains slow down before the collision and subsequently merge and relax to equilibrium. For intermediate velocities no slow down is present before the merger. For high enough velocities the domains can collide and break apart several times before they finally merge. These features leave an imprint on the time evolution of the entropy of the system, which we compute from the area of the dual horizon on the gravity side., Comment: 24 pages, 23 figures

Holography has provided valuable insights into the time evolution of strongly coupled gauge theories in a fixed spacetime. However, this framework is insufficient if this spacetime is dynamical. We present a scheme to evolve a four-dimensional, strongly interacting gauge theory coupled to four-dimensional dynamical gravity in the semiclassical regime. As in previous work, we use holography to evolve the quantum gauge theory stress tensor, whereas the four-dimensional metric evolves according to Einstein's equations coupled to the expectation value of the stress tensor. The novelty of our approach is that both the boundary and the bulk spacetimes are constructed dynamically, one time step at a time. We focus on Friedmann-Lema\^itre-Robertson-Walker geometries and evolve far-from-equilibrium initial states that lead to asymptotically expanding, flat or collapsing Universes, Comment: 16 pages, 6 figures, numerical code available at http://wilkevanderschee.nl/public-codes. v2: matches published version

A pair of complex-conjugate fixed points that lie close to the real axis generates a large mass hierarchy in the real renormalization group flow that passes in between them. We show that pairs of complex fixed points that are close to the real axis and to one another generate multiple hierarchies, some of which can be parametrically enhanced. We illustrate this effect at weak coupling with field-theory examples, and at strong coupling using holography. We also construct complex flows between complex fixed points, including flows that violate the $c$-theorem., Comment: 24 pages + appendices, 12 figures

Cosmological phase transitions proceed via the nucleation of bubbles that subsequently expand and collide. The resulting gravitational wave spectrum depends crucially on the bubble wall velocity. Microscopic calculations of this velocity are challenging even in weakly coupled theories. We use holography to compute the wall velocity from first principles in a strongly coupled, non-Abelian, four-dimensional gauge theory. The wall velocity is determined dynamically in terms of the nucleation temperature. We find an approximately linear relation between the velocity and the ratio $\Delta \mathcal{P}/\mathcal{E}$, with $\Delta \mathcal{P}$ the pressure difference between the inside and the outside of the bubble and $\mathcal{E}$ the energy density outside the bubble. Up to a rescaling, the wall profile is well approximated by that of an equilibrium, phase-separated configuration at the critical temperature. We verify that ideal hydrodynamics provides a good description of the system everywhere except near the wall., Comment: 6 pages, 9 figures. Matches published version in PRD

We use holography to study the dynamics of a strongly-coupled gauge theory in four-dimensional de Sitter space with Hubble rate $H$. The gauge theory is non-conformal with a characteristic mass scale $M$. We solve Einstein's equations numerically and determine the time evolution of homogeneous gauge theory states. If their initial energy density is high compared with $H^4$ then the early-time evolution is well described by viscous hydrodynamics with a non-zero bulk viscosity. At late times the dynamics is always far from equilibrium. The asymptotic late-time state preserves the full de Sitter symmetry group and its dual geometry is a domain-wall in AdS$_5$. The approach to this state is characterised by an emergent relation of the form $\mathcal{P}=w\,\mathcal{E}$ that is different from the equilibrium equation of state in flat space. The constant $w$ does not depend on the initial conditions but only on $H/M$ and is negative if the ratio $H/M$ is close to unity. The event and the apparent horizons of the late-time solution do not coincide with one another, reflecting its non-equilibrium nature. In between them lies an "entanglement horizon" that cannot be penetrated by extremal surfaces anchored at the boundary, which we use to compute the entanglement entropy of boundary regions. If the entangling region equals the observable universe then the extremal surface coincides with a bulk cosmological horizon that just touches the event horizon, while for larger regions the extremal surface probes behind the event horizon., Comment: 45 pages, 13 figures, comments welcome

The existence of phase-separated states is an essential feature of infinite-volume systems with a thermal, first-order phase transition. At energies between those at which the phase transition takes place, equilibrium homogeneous states are either metastable or suffer from a spinodal instability. In this range the stable states are inhomogeneous, phase-separated states. We use holography to investigate how this picture is modified at finite volume in a strongly coupled, four-dimensional gauge theory. We work in the planar limit, $N \to \infty$, which ensures that we remain in the thermodynamic limit. We uncover a rich set of inhomogeneous states dual to lumpy black branes on the gravity side, as well as first- and second-order phase transitions between them. We establish their local (in)stability properties and show that fully non-linear time evolution in the bulk takes unstable states to stable ones., Comment: 69 pages, 31 figures

We use top-down holography to study the thermodynamics of a one-parameter family of three-dimensional, strongly coupled Yang-Mills-Chern-Simons theories with M-theory duals. For generic values of the parameter, the theories exhibit a mass gap but no confinement, meaning no linear quark-antiquark potential. For two specific values of the parameter they flow to an infrared fixed point or to a confining vacuum, respectively. As in the Klebanov-Strassler solution, on the gravity side the mass gap is generated by the smooth collapse to zero size of a cycle in the internal geometry. We uncover a rich phase diagram with thermal phase transitions of first and second order, a triple point and a critical point., Comment: 23 pages, 14 figures

Plasma balls are droplets of deconfined plasma surrounded by a confining vacuum. We present the first holographic simulation of their real-time evolution via the dynamics of localized, finite-energy black holes in the five-dimensional anti-de Sitter (AdS) soliton background. The dual gauge theory is four-dimensional, N=4 super Yang-Mills compactified on a circle with supersymmetry-breaking boundary conditions. We consider horizonless initial data sourced by a massless scalar field. Prompt scalar field collapse then produces an excited black hole at the bottom of the geometry together with gravitational and scalar radiation. The radiation disperses to infinity in the noncompact directions and corresponds to particle production in the dual gauge theory. The black hole evolves toward the dual of an equilibrium plasma ball on a time scale longer than naively expected. This feature is a direct consequence of confinement and is caused by long-lived, periodic disturbances bouncing between the bottom of the AdS soliton and the AdS boundary.

The loss of criticality in the form of weak first-order transitions or the end of the conformal window in gauge theories can be described as the merging of two fixed points that move to complex values of the couplings. When the complex fixed points are close to the real axis, the system typically exhibits walking behavior with Miransky (or Berezinsky-Kosterlitz-Thouless) scaling. We present a novel realization of these phenomena at strong coupling by means of the gauge/gravity duality, and give evidence for the conjectured existence of complex conformal field theories at the fixed points., Comment: 11 pages, 5 figures. v2 matches published version

We have recently shown that the ground state of ${\cal N} = 4$, SU($N_{\rm{\tiny c}}$) super Yang--Mills coupled to $N_{\rm{\tiny f}} \ll N_{\rm{\tiny c}}$ flavors, in the presence of non-zero isospin and R-symmetry charges, is a supersymmetric, superfluid, color superconductor. The holographic description consists of $N_{\rm{\tiny f}}$ D7-brane probes in AdS$_5\times$S$^5$ with electric and instantonic fields on their worldvolume. These correspond to fundamental strings and D3-branes dissolved on the D7-branes, respectively. Here we use this description to determine the spectrum of mesonic excitations. As expected for a charged superfluid we find non-relativistic, massless Goldstone modes. We also find extra ungapped modes that are not associated to the breaking of any global symmetries but to the supersymmetric nature of the ground state. If the quark mass is much smaller than the scale of spontaneous symmetry breaking a pseudo-Goldstone boson is also present. We highlight some new features that appear only for $N_{\rm{\tiny f}}> 2$. We show that, in the generic case of unequal R-symmetry charges, the dissolved strings and D3-branes blow up into a D5-brane supertube stretched between the D7-branes., Comment: 29 pages plus appendices, 8 figures

We use holography to develop a physical picture of the real-time evolution of the spinodal instability of a four-dimensional, strongly-coupled gauge theory with a first-order, thermal phase transition. We numerically solve Einstein's equations to follow the evolution, in which we identify four generic stages: A first, linear stage in which the instability grows exponentially; a second, non-linear stage in which peaks and/or phase domains are formed; a third stage in which these structures merge; and a fourth stage in which the system finally relaxes to a static, phase-separated configuration. On the gravity side the latter is described by a static, stable, inhomogeneous horizon. We conjecture and provide evidence that all static, non-phase separated configurations in large enough boxes are dynamically unstable. We show that all four stages are well described by the constitutive relations of second-order hydrodynamics that include all second-order gradients that are purely spatial in the local rest frame. In contrast, a M\"uller-Israel-Stewart-type formulation of hydrodynamics fails to provide a good description for two reasons. First, it misses some large, purely-spatial gradient corrections. Second, several second-order transport coefficients in this formulation, including the relaxation times $\tau_\pi$ and $\tau_\Pi$, diverge at the points where the speed of sound vanishes., Comment: 45 pages, 35 figures; published version

We study the mass spectrum of spin-0 and spin-2 composite states in a one-parameter family of three-dimensional field theories by making use of their dual descriptions in terms of supergravity. These theories exhibit a mass gap despite being non-confining, and by varying a parameter can be made to flow arbitrarily close to an IR fixed point corresponding to the Ooguri-Park conformal field theory. At the opposite end of parameter space, the dynamics becomes quasi-confining. The glueball spectrum interpolates between these two limiting cases, and for nearly conformal dynamics approaches the result of the Ooguri-Park theory deformed by a relevant operator. In order to elucidate under which circumstances quasi-conformal dynamics leads to the presence of a light pseudo-dilaton, we perform a study of the dependence of the spectrum on the position of a hard-wall IR cutoff and find that, in the present case, the mass of such state is lifted by deep-IR effects., Comment: 28 pages, 8 figures

We use holography to study $d=4$, $\mathcal{N}=4$, SU($N_{\rm \tiny{c}}$) super Yang-Mills coupled to $N_{\rm \tiny{F}} \ll N_{\rm \tiny{c}}$ quark flavors. We place the theory at finite isospin density $n_{\rm \tiny{I}}$ by turning on an isospin chemical potential $\mu_{\rm \tiny{I}}=M_{\rm \tiny{q}}$, with $M_{\rm \tiny{q}}$ the quark mass. We also turn on two R-symmetry charge densities $n_1=n_2$. We show that the ground state is a supersymmetric, superfluid, color superconductor, namely a finite-density state that preserves a fraction of supersymmetry in which part of the global symmetries and part of the gauge symmetries are spontaneously broken. The holographic description consists of $N_{\rm \tiny{F}}$ D7-brane probes in $\mbox{AdS}_5 \times \mbox{S}^5$. The symmetry breaking is due to the dissolution of some D3-branes inside the D7-branes triggered by the electric field associated to the isospin charge. The massless spectrum contains Goldstone bosons and their fermionic superpartners. The massive spectrum contains long-lived, mesonic quasi-particles if $n_{\rm \tiny{I}} \ll \mu_{\rm \tiny{I}}^3$, and no quasi-particles otherwise. We discuss the possibility that, despite the presence of mass scales and charge densities in the theory, conformal and relativistic invariance arise as emergent symmetries in the infrared., Comment: 11 pages, 2 figures. v2: comments and references added, published text

We use holography to analyse relativistic collisions in a one-parameter family of strongly coupled gauge theories with thermal phase transitions. For a critical value of the parameter the transition is second order, for subcritical values it is first order, and for super-critical values it is a smooth crossover. We extract the gauge theory stress tensor from collisions of gravitational shock waves on the dual geometries. Regardless of the nature of the transition, for values of the parameter close to the critical value almost all the energy of the projectiles is deposited into a long-lived, quasi-static blob of energy at mid-rapidity. This configuration is well described by the constitutive relations of second-order hydrodynamics that include all second-order gradients that are purely spatial in the local rest frame. In contrast, a M\"uller-Israel-Stewart-type formulation of hydrodynamics fails to provide a good description. We discuss possible implications for searches of the QCD critical point., Comment: 6 pages, 3 figures

We use holography to study finite-temperature deformations of RG flows that have exotic properties from an RG viewpoint. The holographic model consists of five-dimensional gravity coupled to a scalar field with a potential. Each negative extrema of the potential defines a dual conformal field theory. We find all the black brane solutions on the gravity side and use them to construct the thermal phase diagrams of the dual theories. We find an intricate phase structure that reflects and extends the exotic properties at zero temperature., Comment: 19 pages, 17 figures

We construct the gravity dual of $d=4$, $\mathcal{N}=4$, SU($N_\rm{c}$) super Yang-Mills theory, coupled to $N_\rm{f}$ flavors of dynamical quarks, at non-zero temperature $T$ and non-zero quark density $N_\rm{q}$. The supergravity solutions possess a regular horizon if $T>0$ and include the backreaction of $N_\rm{c}$ color D3-branes and $N_\rm{f}$ flavor D7-branes with $N_\rm{q}$ units of electric flux on their worldvolume. At zero temperature the solutions interpolate between a Landau pole singularity in the ultraviolet and a Lifshitz geometry in the infrared. At high temperature the thermodynamics is directly sensitive to the Landau pole, whereas at low temperature it is not, as expected from effective field theory. At low temperature and sufficiently high charge density we find thermodynamic and dynamic instabilities towards the spontaneous breaking of translation invariance., Comment: 38 pages plus appendices, 25 figures. v2: minor changes, published version. v3: erratum version: conclusions unchanged, discussion and figures modified consequently

We extend our previous analysis of holographic heavy ion collisions in non-conformal theories. We provide a detailed description of our numerical code. We study collisions at different energies in gauge theories with different degrees of non-conformality. We compare four relaxation times: the hydrodynamization time (when hydrodynamics becomes applicable), the EoSization time (when the average pressure approaches its equilibrium value), the isotropization time (when the longitudinal and transverse pressures approach each other) and the condensate relaxation time (when the expectation value of a scalar operator approaches its equilibrium value). We find that these processes can occur in several different orderings. In particular, the condensate can remain far from equilibrium even long after the plasma has hydrodynamized and EoSized. We also explore the rapidity distribution of the energy density at hydrodynamization. This is far from boost-invariant and its width decreases as the non-conformality increases. Nevertheless, the velocity field at hydrodynamization is almost exactly boost-invariant regardless of the non-conformality. This result may be used to constrain the initialization of hydrodynamic fields in heavy ion collisions., Comment: 45 pages, 17 figures. Expanded some sections. Matches published version in JHEP

We use holography to study the spinodal instability of a four-dimensional, strongly-coupled gauge theory with a first-order thermal phase transition. We place the theory on a cylinder in a set of homogeneous, unstable initial states. The dual gravity configurations are black branes afflicted by a Gregory-Laflamme instability. We numerically evolve Einstein's equations to follow the instability until the system settles down to a stationary, inhomogeneous black brane. The dual gauge theory states have constant temperature but non-constant energy density. We show that the time evolution of the instability and the final states are accurately described by second-order hydrodynamics. In the static limit, the latter reduces to a single, second-order, non-linear differential equation from which the inhomogeneous final states can be derived., Comment: 11 pages, 6 figures. Matches published version in JHEP

We revisit a one-parameter family of three-dimensional gauge theories with known supergravity duals. We show that three infrared behaviors are possible. For generic values of the parameter, the theories exhibit a mass gap but no confinement, meaning no linear quark-antiquark potential; for one limiting value of the parameter the theory flows to an infrared fixed point; and for another limiting value it exhibits both a mass gap and confinement. Theories close to these limiting values exhibit quasi-conformal and quasi-confining dynamics, respectively. Eleven-dimensional supergravity provides a simple, geometric explanation of these features., Comment: 35 pages, 9 figures