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Thus far, the known wormholes in string theory connecting disjoint boundaries represented by finite volume quotients of hyperbolic spaces leak: they are non-perturbatively unstable towards brane-anti-brane nucleation in the flux backgrounds that support these wormholes. Turning on additional fluxes suppressed this instability, but would not completely eliminate it. We present the first example of a non-perturbatively stable wormhole in type IIB supergravity on a warped squashed conifold with fluxes., Comment: 12 pages, 1 figure

We extend the computational framework of \cite{Buchel:2023fst} to analysis of shear and bulk viscosities in generic strongly coupled holographic Gauss-Bonnet gauge theories. The finite Gauss-Bonnet coupling constant encodes holographic plasma with non-equal central charges $c\ne a$ at the ultraviolet fixed point. In a simple model we discuss transport coefficients within the causality window $-\frac12\le \frac{c-a}{c}\le \frac 12$ of the theory., Comment: 15 pages, 4 figures

Conformal order are isotropic and translationary invariant thermal states of a conformal theory with nonzero expectation value of certain operators. While ubiquitous in bottom-up models of holographic CFTs, conformal order states are unstable in theories dual to bulk two-derivative gravity. We explore conformal order in strongly coupled theories with gravitational holographic duals involving higher derivative corrections., Comment: 16 pages, 3 figures. arXiv admin note: text overlap with arXiv:2312.05377

We set up a unified framework to efficiently compute the shear and bulk viscosities of strongly coupled gauge theories with gravitational holographic duals involving higher derivative corrections. We consider both Weyl$^4$ corrections, encoding the finite 't Hooft coupling corrections of the boundary theory, and Riemann$^2$ corrections, responsible for non-equal central charges $c\ne a$ of the theory at the ultraviolet fixed point. Our expressions for the viscosities in higher derivative holographic models are extracted from a radially conserved current and depend only on the horizon data., Comment: 46 pages, 10 figures; v2: JHEP version

We use gauge/gravity correspondence to study the gravitational reheating of strongly coupled gauge theories in the rapid exit from the long inflationary (de Sitter) phase. We estimate the maximal reheating temperature of holographic models in $d$-spatial dimensions, which scale invariance is explicitly broken by a source term for an operator ${\cal O}_\Delta$ of dimension $\frac d2+\frac 12< \Delta< d+1$, as well as the top-down ${\cal N}=2^*$ and the cascading gauge theories. The reheating is most efficient when the inflationary phase Hubble constant is much larger than the mass scale of the conformal symmetry breaking of the theory, and for theories with the conformal symmetry breaking operators that are close to marginal., Comment: 18 pages, 3 figures; v2: JHEP version

According to the standard lore, a prolonged inflation leaves a quantum field theory in a cold, low entropy state. Thus, some mechanism is needed to reheat this post-inflationary state, leaving a hot, thermal, radiation-dominated Universe. Typically, reheating is achieved coupling the inflaton field to the QFT degrees of freedom. We argue that the nonequilibrium dynamics of a non-conformal QFT in (post-)inflationary background space-time can produce hot quark-gluon plasma with the reheating temperature of order the inflationary Hubble scale, without the inflaton coupling., Comment: 10 pages, 1 figure. v2: refs and supplemental material added

We use ${\cal N}=2^*$ and cascading gauge theory holographic models to extract the general features of the gravitational susceptibility $\kappa$ of strongly coupled nonconformal quark-gluon plasma. We show that in theories with a relevant coupling constant the gravitational susceptibility is renormalization scheme dependent. We propose to use its temperature derivative, i.e., $\frac{d\kappa}{d\ln T}$, as a scheme-independent characteristic of a QGP. Although $\kappa$ is a thermodynamic quantity, its critical behavior can be drastically distinct in the vicinity of seemingly identical thermal phase transitions., Comment: 23 pages, 6 figures; v2: PRD version

We study stability of the Dynamical Fixed Points (DFPs) of the cascading gauge theory at strong coupling in de Sitter space-time. We compute the spectra of the perturbative fluctuations and identify stable/unstable DFPs, characterized by the ratio of the strong coupling scale $\Lambda$ of the gauge theory and the Hubble constant $H$ of the background space-time. We discover a new phenomenon in the spectrum of gravitational fluctuations of a non-conformal holographic model: distinct branches of the fluctuations for $H\gg \Lambda$ coalesce for sufficiently low $\frac{H}{\Lambda}$, leading to the removal of some excited modes from the spectrum. We establish that, at least in a dual supergravity approximation, cascading gauge theory does not have a stable DFP for $H\in (H_{crit_1},H_{crit_2})$. Initial states of the theory for $H>H_{crit_2}$ evolve to a stable DFP with unbroken chiral symmetry; while for $H< H_{crit_1}$ the states evolve to a de Sitter vacuum with spontaneously broken chiral symmetry., Comment: 90 pages, 14 figures

We develop master equations to study perturbative stability of de Sitter Dynamical Fixed Points (DFPs) of strongly coupled massive quantum field theories in $d+1$ space-time dimensions with a holographic dual. The derived spectrum of linearized fluctuations characterizes the late-time dynamics of holographic strongly coupled non-conformal gauge theories in de Sitter background. Numerous checks and examples are presented., Comment: 26 pages, 2 figures; v2: JHEP version

The holographic duality between cascading gauge theory and type IIB supergravity on warped deformed conifold with fluxes reveals exotic thermal phases with nonzero expectation values of certain operators, persistent to high temperatures. These phases, in the limit of vanishing the strong coupling scale of the cascading gauge theory, would realize thermal ordered conformal phases in relativistic QFTs. We find that the dual Klebanov-Strassler and Klebanov-Tseytlin black branes in this limit are outside the regime of the supergravity approximation, rendering the construction of such conformal ordered states unreliable. While we have been able to construct conformal order in phenomenologically deformed effective theory of type IIB supergravity reduced on warped deformed conifold with fluxes, the removal of the deformation parameter causes the destruction of the thermal conformal ordered phases. Once again, we find that the holographic models with the conformal ordered phases are in the String Theory swampland., Comment: 33 pages, 13 figures; v2: footnote 1 added, JHEP version

Typically, an interactive system evolves towards thermal equilibrium, with hydrodynamics representing a universal framework for its late-time dynamics. Classification of the dynamical fixed points (DFPs) of a driven Quantum Field Theory (with time dependent coupling constants, masses, external background fields, etc.) is unknown. We use holographic framework to analyze such fixed points in one example of strongly coupled gauge theory, driven by homogeneous and isotropic expansion of the background metric - equivalently, a late-time dynamics of the corresponding QFT in Friedmann-Lemaitre-Robertson-Walker Universe. We identify DFPs that are perturbatively stable, and those that are perturbatively unstable, computing the spectrum of the quasinormal modes in the corresponding holographic dual. We further demonstrate that a stable DFP can be unstable non-perturbatively, and explain the role of the entanglement entropy density as a litmus test for a non-perturbative stability. Finally, we demonstrated that a driven evolution might not have a fixed point at all: the entanglement entropy density of a system can grow without bounds., Comment: 48 pages, 19 figures

We study holographic conformal order compactified on $S^3$. The corresponding boundary CFT$ _4$ has a thermal phase with a nonzero expectation value of a certain operator. The gravitational dual to the ordered phase is represented by a black hole in asymptotically $AdS_5$ that violates the no-hair theorem. While the compactification does not destroy the ordered phase, it does not cure its perturbative instability: we identify the scalar channel QNM of the hairy black hole with Im$[w]>0$. On the contrary, we argue that the disordered thermal phase of the boundary CFT is perturbatively stable in holographic models of Einstein gravity and scalars., Comment: 26 pages, 9 figures; v2: typo in (2.15) corrected [thanks to NPB Referee!]

We extend Kodama-Ishibashi and Jansen-Rostworowski-Rutkowski master field framework to study quasinormal modes of black branes and black holes of Einstein gravity in $D=5$ space-time dimensions with multiple scalars and an arbitrary bulk potential. As an application, we consider a thermodynamically unstable state of mass deformed ${\cal N}=4$ supersymmetric Yang-Mills theory at strong coupling. The corresponding gravitational dual is ${\cal N}=2^*$ black brane with a dynamical instability of its translationary invariant horizon. We study the dependence of the quasinormal mode spectra as the boundary gauge theory is compactified on $S^3$ -- the black brane is turned into the black hole., Comment: 41 pages, 16 figures; v2: PRD version

We present a comprehensive analysis of the black holes on warped deformed conifold with fluxes in Type IIB supergravity. These black holes realize the holographic dual to thermal states of the ${\cal N}=1$ supersymmetric $SU(N)\times SU(N+M)$ cascading gauge theory of Klebanov et.al on round $S^3$. There are three distinct mass scales in the theory: the strong coupling scale $\Lambda$ of the cascading gauge theory, the compactification scale $\mu=1/L_3$ (related to the $S^3$ radius $L_3$) and the temperature $T$ of a thermal state. Depending on $\Lambda\,,\, \mu$ and $T$, there is an intricate pattern of confinement/deconfinement (Hawking-Page) and the chiral symmetry breaking phase transitions. In the $S^3\to {\mathbb R}^3$ decompactification limit, $i.e$, $\mu\to 0$, we recover the Klebanov-Tseytlin and the Klebanov-Strassler black branes., Comment: 111 pages, 37 figures; v2: JHEP version

We use holographic correspondence to study transport of the conformal plasma in ${\mathbb R}^{2,1}$ in a phase with a spontaneously broken global $Z_2$ symmetry. The dual black branes in a Poincare patch of asymptotically $AdS_4$ have "hair" -- a condensate of the order parameter for the broken symmetry. This hair affects both the hydrodynamic and the nonhydrodynamic quasinormal modes of the black branes. Nonetheless, the shear viscosity of the conformal order is universal, the bulk viscosity vanishes and the speed of the sound waves is $c_s^2=\frac 12$. We compute the low-lying spectrum of the non-hydrodynamic modes. We identify a quasinormal mode associated with the fluctuations of the $Z_2$ order parameter with the positive imaginary part. The presence of this mode in the spectrum renders the holographic conformal order perturbatively unstable. Correspondingly, the dual black branes violate the correlated stability conjecture., Comment: 34 pages, 13 figures; v2: PRD version

We explore the embedding of the phenomenological holographic models describing thermal relativistic ordered conformal phases in ${\mathbb R}^{2,1}$ in SUGRA/String theory. The dual black branes in a Poincare patch of asymptotically $AdS_4$ have ``hair'' -- a condensate of the order parameter for the broken symmetry. In a gravitational dual the order parameter for a spontaneous symmetry breaking is represented by a bulk scalar field with a nontrivial potential. To construct the ordered conformal phases perturbatively we introduce a phenomenological deformation parameter in the scalar potential. We find that while the ordered phases exist for different values of the deformation parameter, they disappear before the deformation is removed, in one case once the potential is precisely as in the top-down holography. It appears that the holographic models with the conformal ordered phases are in the String theory swampland., Comment: 9 pages, 4 figures

We present a large class of holographic models where the boundary ${\mathbb R}^{2,1}$ dimensional conformal field theory has a thermal phase with a spontaneously broken global symmetry. The dual black branes in a Poincare patch of asymptotically $AdS_4$ violate the no-hair theorem., Comment: 13 pages, 10 figures; v2: typo in eq.23 corrected; v3: NPB version

The Klebanov-Strassler black hole is a holographic dual to ${\cal N}=1$ supersymmetric $SU(N)\times SU(N+M)$ cascading gauge theory plasma with spontaneously broken chiral symmetry. The chiral symmetry breaking sector of the cascading gauge theory contains two dimension-3 operators and a single dimension-7 operator. The black hole solution constructed in arXiv:1809.08484 represents the end point of the instability triggered by the condensation of one of the dimension-3 operators. We study here all three branches of the quasinormal modes of the chiral symmetry breaking sector -- there are no additional instabilities beyond the one identified in arXiv:1012.2404. Thus, the Klebanov-Strassler black hole solution of arXiv:1809.08484 is the only one with homogeneous and isotropic horizon, perturbatively connected to the chirally symmetric Klebanov-Tseytlin black hole arXiv:0706.1768., Comment: 27 pages, 5 figures; v2: NPB version

We use top-down holographic models to study the thermal equation of state of strongly coupled quark-gluon plasma in external magnetic field. We identify different conformal and non-conformal theories within consistent truncations of ${\cal N}=8$ gauged supergravity in five dimensions (including STU models, gauged ${\cal N}=2^*$ theory) and show that the ratio of the transverse to the longitudinal pressure $P_T/P_L$ as a function of $T/\sqrt{B}$ can be collapsed to a 'universal' curve for a wide range of the adjoint hypermultiplet masses $m$. We stress that this does not imply any hidden universality in magnetoresponse, as other observables do not exhibit any universality. Instead, the observed collapse in $P_T/P_L$ is simply due to a strong dependence of the equation of state on the (freely adjustable) renormalization scale: in other words, it is simply a fitting artifact. Remarkably, we do uncover a different universality in ${\cal N}=2^*$ gauge theory in the external magnetic field: we show that magnetized ${\cal N}=2^*$ plasma has a critical point at $T_{crit}/\sqrt{B}$ which value varies by $2\%$ (or less) as $m/\sqrt{B}\in [0,\infty)$. At criticality, and for large values of $m/\sqrt{B}$, the effective central charge of the theory scales as $\propto \sqrt{B}/m$., Comment: 42 pages, 8 figures; v2: JHEP version

${\cal N}=1$ supersymmetric $SU(N)\times SU(N+M)$ cascading gauge theory of Klebanov et.al spontaneously breaks chiral symmetry in Minkowski space-time. We demonstrate that in de Sitter space-time the chiral symmetry breaking occurs for the values of the Hubble constant $H\lesssim 0.7 \Lambda $, as well as in a narrow window $0.92(1) \Lambda \le H\le 0.92(5) \Lambda $. We give a precise definition of the strong coupling scale $\Lambda $ of cascading gauge theory, which is related to the glueball mass scale in the theory $m_{glueball}$ and the asymptotic string coupling $g_s$ as $\Lambda \sim g_s^{1/2} m_{glueball}$., Comment: 94 pages, 26 multi-panel figures; v2: JHEP version

Two recent results indicate that the addition of supersymmetry-breaking ingredients can destabilize the Klebanov-Strassler warped deformed conifold throat. The first comes from an analytic treatment of the interaction between anti-D3 branes and the complex-structure modulus corresponding to the deformation of the conifold [arXiv:1809.06861]. The second comes from the numeric construction of Klebanov-Strassler black holes [arXiv:1809.08484], which stop existing above a certain value of the non-extremality. We show that in both calculations the destabilization energies have the same parametric dependence on $g_s$ and the conifold flux, and only differ by a small numerical factor. This remarkable match confirms that anti-D3 brane uplift can only work in warped throats that have an O(1000) contribution to the D3 tadpole., Comment: 12 pages, 2 figures

de Sitter vacuum of nonconformal gauge theories is non-equilibrium, manifested by a nonvanishing rate of the comoving entropy production at asymptotically late times. This entropy production rate is related to the entanglement entropy of the de Sitter vacuum of the theory. We use holographic correspondence to compute vacuum entanglement entropy density $s_{ent}$ of mass deformed ${\cal N}=4$ supersymmetric Yang-Mills theory - the ${\cal N}=2^*$ gauge theory - for various values of the masses and the coupling constant to the background space-time curvature. For a particular choice of the curvature coupling, the Euclidean model can be solved exactly using the supersymmetric localization. We show that ${\cal N}=2^*$ de Sitter entanglement entropy is not the thermodynamic entropy of the localization free energy at de Sitter temperature. Neither it is related to the thermal entropy of de Sitter vacuum of pair-produced particles., Comment: 38 pages, 8 figures; v2: published version

We construct a black hole solution on warped deformed conifold in type IIB supergravity with fluxes. The black hole has translationary invariant horizon and is a holographic dual to a thermal homogeneous and isotropic state of a cascading $SU(K+P)\times SU(K)$ ${\cal N}=1$ supersymmetric gauge theory with spontaneously broken chiral symmetry. We discuss thermal properties of the new black hole solutions. We comment on implications of the new black hole solutions for the landscape of KKLT de Sitter vacua in string theory., Comment: 14 pages, 3 figures; v2: contains Supplementary material, including the Mathematica scripts and data file necessary to construct KSBH; v3: supplementary material is embedded. arXiv admin note: text overlap with arXiv:1012.2404

Gauge theory/string theory holographic correspondence for ${\cal N}=4$ supersymmetric Yang-Mills theory is well under control in the planar limit, and for large (infinitely large) 't Hooft coupling, $\lambda\to \infty$. Certain aspects of the correspondence can be extended including ${\cal O}(\lambda^{-3/2})$ corrections. There are no reliable first principle computations of the ${\cal N}=4$ plasma non-equilibrium properties beyond the stated order. We show extreme sensitivity of the non-hydrodynamic spectra of holographic ${\cal N}=4$ SYM plasma to ${\cal O}(\lambda^{-3})$ corrections, challenging any conclusions reached from 'resummation' of ${\cal O}(\lambda^{-3/2})$ corrections., Comment: 10 pages, 2 figures; v2: PRD version (rapid communications)

Relativistic fluid hydrodynamics, organized as an effective field theory in the velocity gradients, has zero radius of convergence due to the presence of non-hydrodynamic excitations. Likewise, the theory of elasticity of brittle solids, organized as an effective field theory in the strain gradients, has zero radius of convergence due to the process of the thermal nucleation of cracks. Viscoelastic materials share properties of both fluids and solids. We use holographic gauge theory/gravity correspondence to study all order hydrodynamics of relativistic viscoelastic media., Comment: published version

We study hydrodynamics of four-dimensional non-conformal holographic plasma with non-equal central charges $c\ne a$ at the ultraviolet fixed point. We compute equation of state, the speed of sound waves, transport coefficients (shear and bulk viscosities), and discuss causality. We study the asymptotic character of the hydrodynamic series for the homogeneous and isotropic expansion of the plasma. We perform computations for finite $c-a\ne 0$, but to leading nonvanishing order in the conformal symmetry breaking coupling., Comment: 25 pages, 10 figures; v2: references added

Hydrodynamics is a universal effective theory describing relaxation of quantum field theories towards equilibrium. Massive QFTs in de Sitter spacetime are never at equilibrium. We use holographic gauge theory/gravity correspondence to describe relaxation of a QFT to its Bunch-Davies vacuum - an attractor of its late-time dynamics. Specifically, we compute the analogue of the quasinormal modes describing the relaxation of a holographic toy model QFT in de Sitter., Comment: 19 pages, 6 figures, 1 supplemental file

We study the effects of supersymmetry on singularity development scenario in holography presented in \cite{Bosch:2017ccw} (BBL). We argue that the singularity persists in a supersymmetric extension of the BBL model. The challenge remains to find a string theory embedding of the singularity mechanism., Comment: 33 pages, 16 figures

In holographic applications one can encounter scenarios where a long-wavelength instability can arise. In such situations, it is often the case that the dynamical end point of the instability is a new equilibrium phase with a nonlinear scalar hair condensate outside the black hole horizon. We here review holographic setups where symmetric horizons suffer from long-wavelength instabilities where a suitable equilibrium condensate phase does not exist. We study the dynamics of the simplest model in this exotic class, and show that it uncovers arbitrarily large curvatures in the vicinity of the horizon which asymptotically turn such region singular, at finite time with respect to the boundary theory., Comment: 38 pages, 41 figures

Verlinde argued \cite{Verlinde:2016toy} that baryonic matter in de Sitter Universe with a Hubble constant $H$ produces a bulk contribution to the vacuum entanglement entropy $\delta S_{ent}$. Using the de Sitter temperature $T_{dS}=\frac{H}{2\pi}$, he interpreted $\delta M$ in the first law $T_{dS}\ \delta S_{ent}=-\delta M$ with the Dark Matter energy. We use standard tools of the gauge/gravity correspondence to present some evidence for the Verlinde's proposal., Comment: 5 pages, 1 figure

We use holographic correspondence to argue that Euclidean (Bunch-Davies) vacuum is a late-time attractor of the dynamical evolution of quantum gauge theories at strong coupling. The Bunch-Davies vacuum is not an adiabatic state, if the gauge theory is non-conformal --- the comoving entropy production rate is nonzero. Using the N=2* gauge theory holography, we explore prospects of explaining current accelerated expansion of the Universe as due to the vacuum energy of a strongly coupled QFT., Comment: 35 pages, 8 figures; v3: JHEP version

Microseconds after the Big Bang quarks and gluons formed a strongly-coupled non-conformal liquid driven out-of-equilibrium by the expansion of the Universe. We use holography to determine the non-equilibrium behavior of this liquid in a Friedmann-Lemaitre-Robertson-Walker Universe and develop an expansion for the corresponding entropy production in terms of the derivatives of the cosmological scale factor. We show that the resulting series has zero radius of convergence and we discuss its resurgent properties. Finally, we compute the resummed entropy production rate in de Sitter Universe at late times and show that the leading order approximation given by bulk viscosity effects can strongly overestimate/underestimate the rate depending on the microscopic parameters., Comment: 7 pages, 1 figure; v2: various improvements in presentation, title changed by journal, matches the published version

Boson stars are stationary soliton-like gravitational configurations supported by a complex scalar field charged under the global $U(1)$ symmetry. We discuss properties of boson stars in type IIB supergravity approximation to string theory. A notable difference is that in supergravity models the global symmetry of the complex scalar field is gauged. We focus on global asymptotically $AdS_5$ space-time, where the boson stars are expected to represent stable low-energy non-thermal excitations in holographically dual quiver conformal gauge theory., Comment: 21 pages, 6 figures

$AdS_5$ type IIb supergravity compactifications on five-dimensional Einstein manifolds ${\cal V}_5$ realize holographic duals to four-dimensional conformal field theories. Black holes in such geometries are dual to thermal states in these CFTs. When black holes become sufficiently small in (global) $AdS_5$, they are expected to suffer Gregory-Laflamme instability with respect to localization on ${\cal V}_5$. Previously, the instability was demonstrated for gravitational dual of ${\cal N}=4$ SYM, where ${\cal V}_5=S^5$. We extend stability analysis to arbitrary ${\cal V}_5$. We point out that the quasinormal mode equation governing the instabilities is universal. The precise onset of the instability is ${\cal V}_5$-sensitive, as it is governed by the lowest non-vanishing eigenvalue $\lambda_{min}$ of its Laplacian., Comment: 11 pages, 2 figures

Low-energy thermal equilibrium states of strongly coupled ${\cal N}=4$ supersymmetric Yang-Mills (SYM) theory on a three-sphere are unstable with respect to fluctuations breaking the global $SO(6)$ R-symmetry. Using the gauge theory/gravity correspondence, a large class of initial conditions in the R-symmetry singlet sector of the theory was been identified that fail to thermalize \cite{Buchel:2013uba,Balasubramanian:2014cja}. A toy model realization of such states is provided by {\it boson stars}, a stationary gravitational configurations supported by a complex scalar field in $AdS_5$-gravity. Motivated by the SYM example, we extend the boson star toy model to include the global $SO(6)$ R-symmetry. We show that sufficient light boson stars in the R-symmetry singlet sector are stable with respect to linearized fluctuations. As the mass of the boson star increases, they do suffer tachyonic instability associated with their localization on $S^5$. This is opposite to the behaviour of small black holes (dual to equilibrium states of ${\cal N}=4$ SYM) in global $AdS_5$: the latter develop tachyonic instability as they become sufficiently light. Based on analogy with light boson stars, we expect that the R-symmetry singlet nonthermal states in strongly coupled gauge theories, represented by the quasiperiodic solutions of \cite{Balasubramanian:2014cja}, are stable with respect to linearized fluctuations breaking the R-symmetry., Comment: 17 pages, 2 figures; typos corrected and references added

We respond to the criticisms of a recent comment by Bizo\'n and Rostworowski [arXiv:1410.2631]., Comment: 2 pages, 1 figure

We use top-down gauge theory/string theory correspondence to compute relaxation rates in strongly coupled nonconformal gauge theory plasma. We compare models with difference mechanisms of breaking the scale invariance: "hard breaking" (by relevant operators) and "soft breaking" (by marginal operators). We find that the thermalization time of the transverse traceless fluctuations of the stress-energy tensor is rather insensitive to the mechanisms of breaking the scale invariance over a large range of the scale-breaking parameter $\delta=\frac 13-c_s^2$. We comment on the relevance of the results to QCD quark-gluon plasma., Comment: 12 pages, 3 figures. arXiv admin note: text overlap with arXiv:1108.6070

We initiate the study of equilibration rates of strongly coupled quark-gluon plasmas in the absence of conformal symmetry. We primarily consider a supersymmetric mass deformation within ${\cal N}=2^{*}$ gauge theory and use holography to compute quasinormal modes of a variety of scalar operators, as well as the energy-momentum tensor. In each case, the lowest quasinormal frequency, which provides an approximate upper bound on the thermalization time, is proportional to temperature, up to a pre-factor with only a mild temperature dependence. We find similar behaviour in other holographic plasmas, where the model contains an additional scale beyond the temperature. Hence, our study suggests that the thermalization time is generically set by the temperature, irrespective of any other scales, in strongly coupled gauge theories., Comment: 6 pages, 7 figures

We consider small black holes in $AdS_5\times S^5$, smeared on $S^5$. We compute the spectrum of $\ell \in [1,10]$ $S^5$-quasinormal modes corresponding to fluctuations leading to localization of these black holes on $S^5$. We recover the zero mode found by Hubeny and Rangamani (HR) previously \cite{Hubeny:2002xn}, and explicitly demonstrate that a Gregory-Laflamme type instability is at play in this system. The instability is associated with the expectation value of a dimension-5 operator., Comment: 16 pages, 1 figure; v2: CQG published version (20 pages, 2 figures)

For a closed system to equilibrate from a given initial condition there must exist an equilibrium state with the energy equal to the initial one. Equilibrium states of a strongly coupled gauge theory with a gravitational holographic dual are represented by black holes. We study the spectrum of black holes in Pilch-Warner geometry. These black holes are holographically dual to equilibrium states of strongly coupled $SU(N)$ ${\cal N}=2^*$ gauge theory plasma on $S^3$ in the planar limit. We find that there is no energy gap in the black hole spectrum. Thus, there is a priory no obstruction for equilibration of arbitrary low-energy states in the theory via a small black hole gravitational collapse. The latter is contrasted with phenomenological examples of holography with dual four-dimensional CFTs having non-equal central charges in the stress-energy tensor trace anomaly., Comment: 34 pages, 6 figures; v2: NPB published version (31 pages, 5 figures)

We consider the dynamics of a spherically symmetric massless scalar field coupled to general relativity in Anti--de Sitter spacetime in the small-amplitude limit. Within the context of our previously developed two time framework (TTF) to study the leading self-gravitating effects, we demonstrate the existence of two new conserved quantities in addition to the known total energy $E$ of the modes: The particle number $N$ and Hamiltonian $H$ of our TTF system. Simultaneous conservation of $E$ and $N$ implies that weak turbulent processes undergo dual cascades (direct cascade of $E$ and inverse cascade of $N$ or vice versa). This partially explains the observed dynamics of 2-mode initial data. In addition, conservation of $E$ and $N$ limits the region of phase space that can be explored within the TTF approximation and in particular rules out equipartion of energy among the modes for general initial data. Finally, we discuss possible effects of conservation of $N$ and $E$ on late time dynamics., Comment: 9 pages, 2 figures; V2: minor updates; V3: updates to match version accepted for publication

We describe the application of pseudo-spectral methods to problems of holographic thermal quenches of relevant couplings in strongly coupled gauge theories. We focus on quenches of a fermionic mass term in a strongly coupled N=4 supersymmetric Yang-Mills plasma, and the subsequent equilibration of the system. From the dual gravitational perspective, we study the gravitational collapse of a massive scalar field in asymptotically anti-de Sitter geometry with a prescribed boundary condition for its non-normalizable mode. Access to the full background geometry of the gravitational collapse allows for the study of nonlocal probes of the thermalization process. We discuss the evolution of the apparent and the event horizons, the two-point correlation functions of operators of large conformal dimensions, and the evolution of the entanglement entropy of the system. We compare the thermalization process from the viewpoint of local (the one-point) correlation functions and these nonlocal probes, finding that the thermalization time as measured by the probes is length dependent, and approaches the thermalization time of the one-point function for longer probes. We further discuss how the different energy scales of the problem contribute to its thermalization., Comment: 83 pages, 25 figures. v2: Corrected constraint in equation (A.26), which led to non-monotonic apparent horizons in our simulations. Replaced most figures. Added equation (4.11). Added references [37], [38]. Added acknowledgement. Corrected some typos. Most conclusions remain unchanged

Motivated by a low-energy effective description of gauge theory/string theory duality, we conjecture that the dynamics of $SO(4)$-invariant states in a large class of four-dimensional conformal gauge theories on $S^3$ with non-equal central charges $c\ne a$ are universal on time scales $t_{\rm universal}\propto ({\cal E}-{\cal E}_{\rm vacuum})^{-1}$, in the limit where the energy ${\cal E}\to {\cal E}_{\rm vacuum}$. We show that low-energy excitations in $c\ne a$ CFTs do not thermalize in this limit. The holographic universality conjecture then implies that within the Einstein-scalar field system (dual to theories with $c=a$), $AdS_5$ is stable to spherically symmetric perturbations against formation of trapped surfaces within time scales $t_{\rm universal}$., Comment: 12 pages; v2: reference added

We discuss consistent truncations of type IIB supergravity on resolved warped deformed conifolds with fluxes. These actions represent the gravitational duals to the baryonic branch deformation of the Klebanov-Strassler cascading gauge theory. As an application, we demonstrate that the baryonic branch is lifted in cascading gauge theory plasma., Comment: v1: 16 pages, 1 figure; v2: 21 pages, 1 figure; v3: reference added

For a real massless scalar field in general relativity with a negative cosmological constant, we uncover a large class of spherically symmetric initial conditions that are close to AdS, but whose numerical evolution does not result in black hole formation. According to the AdS/CFT dictionary, these bulk solutions are dual to states of a strongly interacting boundary CFT that fail to thermalize at late times. Furthermore, as these states are not stationary, they define dynamical CFT configurations that do not equilibrate. We develop a two-timescale perturbative formalism that captures both direct and inverse cascades of energy and agrees with our fully nonlinear evolutions in the appropriate regime. We also show that this formalism admits a large class of quasi-periodic solutions. Finally, we demonstrate a striking parallel between the dynamics of AdS and the classic Fermi-Pasta-Ulam-Tsingou problem., Comment: v2: Added Supplementary Material addressing approximations and code validation; several improvements to Letter. Letter: 5 pages, 4 figures. Supplementary Material: 3 pages, 4 figures

Although Pilch-Warner (PW) gravitational renormalization group flow [arXiv:hep-th/0004063] passes a number of important consistency checks to be identified as a holographic dual to a large-$N$ $SU(N)$ ${\cal N}=2^*$ supersymmetric gauge theory, it fails to reproduce the free energy of the theory on $S^4$, computed with the localization techniques. This disagreement points to the existence of a larger dual gravitational consistent truncation, which in the gauge theory flat-space limit reduces to a PW flow. Such truncation was recently identified by Bobev-Elvang-Freedman-Pufu (BEFP) [arXiv:1311.1508]. Additional bulk scalars of the BEFP gravitation truncation might lead to destabilization of the finite-temperature deformed PW flows, and thus modify the low-temperature thermodynamics and hydrodynamics of ${\cal N} =2^*$ plasma. We compute the quasinormal spectrum of these bulk scalar fields in the thermal PW flows and demonstrate that these modes do not condense, as long as the masses of the ${\cal N}=2^*$ hypermultiplet components are real., Comment: 13 pages, 2 figures; supplemental files attached

Placing anti-D3 branes at the tip of the conifold in Klebanov-Strassler geometry provides a generic way of constructing meta-stable de Sitter (dS) vacua in String Theory. A local geometry of such vacua exhibit gravitational solutions with a D3 charge measured at the tip opposite to the asymptotic charge. We discuss a restrictive set of such geometries, where anti-D3 branes are smeared at the tip. Such geometries represent holographic dual of cascading gauge theory in dS4 with or without chiral symmetry breaking. We find that in the phase with unbroken chiral symmetry the D3 charge at the tip is always positive. Furthermore, this charge is zero in the phase with spontaneously broken chiral symmetry. We show that the effective potential of the chirally symmetric phase is lower than that in the symmetry broken phase, i.e, there is no spontaneous chiral symmetry breaking for cascading gauge theory in dS4. The positivity of the D3 brane charge in smooth de-Sitter deformed conifold geometries with fluxes presents difficulties in uplifting AdS vacua to dS ones in String Theory via smeared anti-D3 branes., Comment: 47 pages, 6 figures. v2: published version. arXiv admin note: substantial text overlap with arXiv:1108.6070

We make an analytic investigation of rapid quenches of relevant operators in d-dimensional holographic CFT's, which admit a dual gravity description. We uncover a universal scaling behaviour in the response of the system, which depends only on the conformal dimension of the quenched operator in the vicinity of the ultraviolet fixed point of the theory. Unless the amplitude of the quench is scaled appropriately, the work done on a system during the quench diverges in the limit of abrupt quenches for operators with dimension $\frac{d}{2} \le\Delta < d$., Comment: 6 pages, 4 figures

We compare exact results from Pestun's localization of SU(N) N=2^* gauge theory on S^4 with available holographic models. While localization can explain the Coulomb branch vacuum of the holographic Pilch-Warner flow, it disagrees with the holographic Gauntlett et.al vacuum of N=2 super Yang-Mills theory. We further compute the free energy of the Pilch-Warner flow on S^4 and show that it disagrees with the localization result both for a finite S^4 radius, and in the S^4 decompactification limit. Thus, neither model represents holographic dual of supersymmetric S^4 localization of Pestun., Comment: 23 pages, 3 figures; v2: references and a note added

We construct boson stars in global Anti de Sitter (AdS) space and study their stability. Linear perturbation results suggest that the ground state along with the first three excited state boson stars are stable. We evolve some of these solutions and study their nonlinear stability in light of recent work \cite{Bizon:2011gg} arguing that a weakly turbulent instability drives scalar perturbations of AdS to black hole formation. However evolutions suggest that boson stars are nonlinearly stable and immune to the instability for sufficiently small perturbation. Furthermore, these studies find other families of initial data which similarly avoid the instability for sufficiently weak parameters. Heuristically, we argue that initial data families with widely distributed mass-energy distort the spacetime sufficiently to oppose the coherent amplification favored by the instability. From the dual CFT perspective our findings suggest that there exist families of rather generic initial conditions in strongly coupled CFT (with large number of degrees of freedom) that do not thermalize in the infinite future., Comment: 32 pages, 12 figures; Updated with a few more references and typos fixed