46 research outputs found
Inhomogeneous holographic thermalization
The sudden injection of energy in a strongly coupled conformal field theory
and its subsequent thermalization can be holographically modeled by a shell
falling into anti-de Sitter space and forming a black brane. For a homogeneous
shell, Bhattacharyya and Minwalla were able to study this process analytically
using a weak field approximation. Motivated by event-by-event fluctuations in
heavy ion collisions, we include inhomogeneities in this model, obtaining
analytic results in a long wavelength expansion. In the early-time window in
which our approximations can be trusted, the resulting evolution matches well
with that of a simple free streaming model. Near the end of this time window,
we find that the stress tensor approaches that of second-order viscous
hydrodynamics. We comment on possible lessons for heavy ion phenomenology.Comment: 53 pages, 10 figures; v2: references adde
Inhomogeneous Thermalization in Strongly Coupled Field Theories
To describe theoretically the creation and evolution of the quark-gluon
plasma, one typically employs three ingredients: a model for the initial state,
non-hydrodynamic early time evolution, and hydrodynamics. In this paper we
study the non-hydrodynamic early time evolution using the AdS/CFT
correspondence in the presence of inhomogeneities. We find that the AdS
description of the early time evolution is well-matched by free streaming. Near
the end of the early time interval where our analytic computations are
reliable, the stress tensor agrees with the second order hydrodynamic stress
tensor computed from the local energy density and fluid velocity. Our
techniques may also be useful for the study of far-from-equilibrium strongly
coupled systems in other areas of physics.Comment: 5 pages, 3 figures; v2: minor clarifications and reference adde
Holographic Second Laws of Black Hole Thermodynamics
Recently, it has been shown that for out-of-equilibrium systems, there are additional constraints on thermodynamical evolution besides the ordinary second law. These form a new family of second laws of thermodynamics, which are equivalent to the monotonicity of quantum Rényi divergences. In black hole thermodynamics, the usual second law is manifest as the area increase theorem. Hence one may ask if these additional laws imply new restrictions for gravitational dynamics, such as for out-of-equilibrium black holes? Inspired by this question, we study these constraints within the AdS/CFT correspondence. First, we show that the Rényi divergence can be computed via a Euclidean path integral for a certain class of excited CFT states. Applying this construction to the boundary CFT, the Rényi divergence is evaluated as the renormalized action for a particular bulk solution of a minimally coupled gravity-scalar system. Further, within this framework, we show that there exist transitions which are allowed by the traditional second law, but forbidden by the additional thermodynamical constraints. We speculate on the implications of our findings
Holographic Thermalization
Using the AdS/CFT correspondence, we probe the scale-dependence of
thermalization in strongly coupled field theories following a quench, via
calculations of two-point functions, Wilson loops and entanglement entropy in
d=2,3,4. In the saddlepoint approximation these probes are computed in AdS
space in terms of invariant geometric objects - geodesics, minimal surfaces and
minimal volumes. Our calculations for two-dimensional field theories are
analytical. In our strongly coupled setting, all probes in all dimensions share
certain universal features in their thermalization: (1) a slight delay in the
onset of thermalization, (2) an apparent non-analyticity at the endpoint of
thermalization, (3) top-down thermalization where the UV thermalizes first. For
homogeneous initial conditions the entanglement entropy thermalizes slowest,
and sets a timescale for equilibration that saturates a causality bound over
the range of scales studied. The growth rate of entanglement entropy density is
nearly volume-independent for small volumes, but slows for larger volumes.Comment: 39 pages, 24 figure
Particle Production near an AdS Crunch
We numerically study the dual field theory evolution of five-dimensional
asymptotically anti-de Sitter solutions of supergravity that develop
cosmological singularities. The dual theory is an unstable deformation of the N
= 4 gauge theory on R S3, and the big crunch singularity in the bulk
occurs when a boundary scalar field runs to infinity. Consistent quantum
evolution requires one imposes boundary conditions at infinity. Modeling these
by a steep regularization of the scalar potential, we find that when an
initially nearly homogeneous wavepacket rolls down the potential, most of the
potential energy of the initial configuration is converted into gradient energy
during the first oscillation of the field. This indicates there is no
transition from a big crunch to a big bang in the bulk for dual boundary
conditions of this kind.Comment: 20 pages, 6 figure
New stable phase of non uniform black strings in
We consider the non uniform black string equations in arbitrary number
of dimension in a perturbative approach up to order 2 and in a non
perturbative. We restrict the study in the perturbative approach to the
backreacting modes, since they provide the first relevant corrections on the
thermodynamical quantities of the solutions. We also present some preliminary
results in the construction of non-perturbative solutions, in particular, we
present a first part of the non uniform - uniform black string phase diagram.
Our results suggests the existence of a new stable phase for non uniform
black strings, namely long non uniform black string, with the extra direction
length of the order of the curvature.Comment: Results extended. 14 pages, 5 figure
D-Brane Potentials from Multi-Trace Deformations in AdS/CFT
It is known that certain AdS boundary conditions allow smooth initial data to
evolve into a big crunch. To study this type of cosmological singularity, one
can use the dual quantum field theory, where the non-standard boundary
conditions are reflected by the presence of a multi-trace potential unbounded
below. For specific AdS_4 and AdS_5 models, we provide a D-brane (or M-brane)
interpretation of the unbounded potential. Using probe brane computations, we
show that the AdS boundary conditions of interest cause spherical branes to be
pushed to the boundary of AdS in finite time, and that the corresponding
potential agrees with the multi-trace deformation of the dual field theory.
Systems with expanding spherical D3-branes are related to big crunch
supergravity solutions by a phenomenon similar to geometric transition.Comment: 26 pages, 3 figures, v4: a few typos fixed
New AdS solitons and brane worlds with compact extra-dimensions
We construct new static, asymptotically AdS solutions where the conformal
infinity is the product of Minkowski spacetime and a sphere . Both
globally regular, soliton-type solutions and black hole solutions are
considered. The black holes can be viewed as natural AdS generalizations of the
Schwarzschild black branes in Kaluza-Klein theory. The solitons provide new
brane-world models with compact extra-dimensions. Different from the
Randall-Sundrum single-brane scenario, a Schwarzschild black hole on the Ricci
flat part of these branes does not lead to a naked singularity in the bulk.Comment: 28 pages, 4 figure