Stability of Charged Global AdS4_4 Spacetimes

We study linear and nonlinear stability of asymptotically AdS$_4$ solutions in Einstein-Maxwell-scalar theory. After summarizing the set of static solutions we first examine thermodynamical stability in the grand canonical ensemble and the phase transitions that occur among them. In the second part of the paper we focus on nonlinear stability in the microcanonical ensemble by evolving radial perturbations numerically. We find hints of an instability corner for vanishingly small perturbations of the same kind as the ones present in the uncharged case. Collapses are avoided, instead, if the charge and mass of the perturbations come to close the line of solitons. Finally we examine the soliton solutions. The linear spectrum of normal modes is not resonant and instability turns on at extrema of the mass curve. Linear stability extends to nonlinear stability up to some threshold for the amplitude of the perturbation. Beyond that, the soliton is destroyed and collapses to a hairy black hole. The relative width of this stability band scales down with the charge Q, and does not survive the blow up limit to a planar geometry.Comment: 43 pg, 22 fig. Published version. Appendix adde

Holographic thermalization in finite-size systems

The AdS/CFT correspondence has provided a fascinating window into the real-time dynamics of strongly-coupled QFTs. On the other hand, studies of gravitational collapse in asymptotically global AdS spacetimes have unraveled a surprisingly rich landscape of possible routes to final black hole formation or its absence thereof, that depend both on the precise dynamics and the initial state considered. In the light of the equivalence between gravitational collapse and thermalization implied by the duality, it is natural to wonder which universal lessons these results entail on the out-of-equilibrium physics of isolated, macroscopic quantum systems at strong coupling. This thesis aims to be a modest step in elucidating this question

Convergence of the Fefferman-Graham expansion and complex black hole anatomy

Given a set of sources and one-point function data for a Lorentzian holographic QFT, does the Fefferman-Graham expansion converge? If it does, what sets the radius of convergence, and how much of the interior of the spacetime can be reconstructed using this expansion? As a step towards answering these questions we consider real analytic CFT data, where in the absence of logarithms, the radius is set by singularities of the complex metric reached by analytically continuing the Fefferman-Graham radial coordinate. With the conformal boundary at the origin of the complex radial plane, real Lorentzian submanifolds appear as piecewise paths built from radial rays and arcs of circles centred on the origin. This allows singularities of Fefferman-Graham metric functions to be identified with gauge-invariant singularities of maximally extended black hole spacetimes, thereby clarifying the physical cause of the limited radius of convergence in such cases. We find black holes with spacelike singularities can give a radius of convergence equal to the horizon radius, however for black holes with timelike singularities the radius is smaller. We prove that a finite radius of convergence does not necessarily follow from the existence of an event horizon, a spacetime singularity, nor from caustics of the Fefferman-Graham gauge, by providing explicit examples of spacetimes with an infinite radius of convergence which contain such features.Comment: 29 pages + appendices, 13 figure

Holographic Relaxation of Finite Size Isolated Quantum Systems

We study holographically the out of equilibrium dynamics of a finite size closed quantum system in 2+1 dimensions, modelled by the collapse of a shell of a massless scalar field in AdS4. In global coordinates there exists a variety of evolutions towards final black hole formation which we relate with different patterns of relaxation in the dual field theory. For large scalar initial data rapid thermalization is achieved as a priori expected. Interesting phenomena appear for small enough amplitudes. Such shells do not generate a black hole by direct collapse, but quite generically an apparent horizon emerges after enough bounces off the AdS boundary. We relate this bulk evolution with relaxation processes at strong coupling which delay in reaching an ergodic stage. Besides the dynamics of bulk fields, we monitor the entanglement entropy, finding that it oscillates quasi-periodically before final equilibration. The radial position of the traveling shell is brought into correspondence with the evolution of the entanglement pattern in the dual field theory. The entanglement entropy is not only able to portrait the streaming of entangled excitations, but it is also a useful probe of interaction effects.Comment: 37 pages, 27 figure

Collapse and Revival in Holographic Quenches

We study holographic models related to global quantum quenches in finite size systems. The holographic set up describes naturally a CFT, which we consider on a circle and a sphere. The enhanced symmetry of the conformal group on the circle motivates us to compare the evolution in both cases. Depending on the initial conditions, the dual geometry exhibits oscillations that we holographically interpret as revivals of the initial field theory state. On the sphere, this only happens when the energy density created by the quench is small compared to the system size. However on the circle considerably larger energy densities are compatible with revivals. Two different timescales emerge in this latter case. A collapse time, when the system appears to have dephased, and the revival time, when after rephasing the initial state is partially recovered. The ratio of these two times depends upon the initial conditions in a similar way to what is observed in some experimental setups exhibiting collapse and revivals

Rigorous bounds on transport from causality

We use causality to derive a number of simple and universal constraints on dispersion relations, which describe the location of singularities of retarded two-point functions in relativistic quantum field theories. We prove that all causal dissipative dispersion relations have a finite radius of convergence. We then give two-sided bounds on all transport coefficients in units of this radius, including an upper bound on diffusivity.Comment: 4 pages. New relational bound on sound attenuation, improved test function, references adde

Holographic quenches with a gap

In order to holographically model quenches with a gapped final hamiltonian, we consider a gravity-scalar theory in anti-de Sitter space with an infrared hard wall. We allow a time dependent profile for the scalar field at the wall. This induces an energy exchange between bulk and wall and generates an oscillating scalar pulse. We argue that such backgrounds are the counterpart of quantum revivals in the dual field theory. We perform a qualitative comparison with the quench dynamics of the massive Schwinger model, which has been recently analyzed using tensor network techniques. Agreement is found provided the width of the oscillating scalar pulse is inversely linked to the energy density communicated by the quench. We propose this to be a general feature of holographic quenches.The work of E.daS. is nanced by the spanish grant BES-2013-063972. E.L. has been supported by the spanish grant FPA2012-32828 and SEV-2012-0249 of the Centro de Excelencia Severo Ochoa Programme. The work of J.M. is supported in part by the spanish grant FPA2011-22594, by Xunta de Galicia (GRC2013- 024), by the Consolider-CPAN (CSD2007-00042), and by FEDER. A.S. is supported by the European Research Council grant HotLHC ERC-2011-StG-279579 and by Xunta de Galicia (Conselleria de Educaci on). Part of the numerical calculations were performed at the Centro de Supercomputaci on de Galicia (CESGA).S

Transseries for causal diffusive systems

The large proper-time behaviour of expanding boost-invariant fluids has provided many crucial insights into quark-gluon plasma dynamics. Here we formulate and explore the late-time behaviour of nonequilibrium dynamics at the level of linearized perturbations of equilibrium, but without any special symmetry assumptions. We introduce a useful quantitative approximation scheme in which hydrodynamic modes appear as perturbative contributions while transients are nonperturbative. In this way, solutions are naturally organized into transseries as they are in the case of boost-invariant flows. We focus our attention on the ubiquitous telegrapher's equation, the simplest example of a causal theory with a hydrodynamic sector. In position space we uncover novel transient contributions as well as Stokes phenomena which change the structure of the transseries based on the spacetime region or the choice of initial data.Comment: 23 pages + appendices, 16 figure

Floquet scalar dynamics in global AdS

We study periodically driven scalar fields and the resulting geometries with global AdS asymptotics. These solutions describe the strongly coupled dynamics of dual finite-size quantum systems under a periodic driving which we interpret as Floquet condensates. They span a continuous two-parameter space that extends the linearized solutions on AdS. We map the regions of stability in the solution space. In a significant portion of the unstable subspace, two very different endpoints are reached depending upon the sign of the perturbation. Collapse into a black hole occurs for one sign. For the opposite sign instead one attains a regular solution with periodic modulation. We also construct quenches where the driving frequency and amplitude are continuously varied. Quasistatic quenches can interpolate between pure AdS and sourced solutions with time periodic vev. By suitably choosing the quasistatic path one can obtain boson stars dual to Floquet condensates at zero driving field. We characterize the adiabaticity of the quenching processes. Besides, we speculate on the possible connections of this framework with time crystals.This work of was supported by grants FPA2014-52218-P from Ministerio de Economia y Competitividad, by Xunta de Galicia ED431C 2017/07, by FEDER and by Grant Mar a de Maeztu Unit of Excellence MDM-2016-0692. A.S. is happy to acknowledge support from the International Centre for Theoretical Sciences (ICTS-TIFR), and wants to express his gratitude to the ICTS community, and especially to the String Theory Group, for their warm welcome. D.M. thanks the FRont Of pro-Galician Scientists (FROGS) for unconditional support. A.B. thanks the support of the Spanish program \Ayudas para contratos predoctorales para la formaci on de doctores 2015" associated to FPA2014-52218-P. This research has benefited from the use computational resources/services provided by the Galician Supercomputing Centre (CESGA).S