95 research outputs found
Strong subadditivity and the covariant holographic entanglement entropy formula
Headrick and Takayanagi showed that the Ryu-Takayanagi holographic
entanglement entropy formula generally obeys the strong subadditivity (SSA)
inequality, a fundamental property of entropy. However, the Ryu-Takayanagi
formula only applies when the bulk spacetime is static. It is not known whether
the covariant generalization proposed by Hubeny, Rangamani, and Takayanagi
(HRT) also obeys SSA. We investigate this question in three-dimensional
AdS-Vaidya spacetimes, finding that SSA is obeyed as long as the bulk spacetime
satisfies the null energy condition. This provides strong support for the
validity of the HRT formula.Comment: 38 page
Meson Thermalization in Various Dimensions
In gauge/gravity duality framework the thermalization of mesons in strongly
coupled (p+1)-dimensional gauge theories is studied for a general Dp-Dq system,
q>=p, using the flavour Dq-brane as a probe. Thermalization corresponds to the
horizon formation on the flavour Dq-brane. We calculate the thermalization
time-scale due to a time-dependent change in the baryon number chemical
potential, baryon injection in the field theory. We observe that for such a
general system it has a universal behaviour depending only on the t'Hooft
coupling constant and the two parameters which describe how we inject baryons
into the system. We show that this universal behaviour is independent of the
details of the theory whether it is conformal and/or supersymmetric.Comment: 26 pages, 2 figure
Thermalization from gauge/gravity duality: Evolution of singularities in unequal time correlators
We consider a gauge/gravity dual model of thermalization which consists of a
collapsing thin matter shell in asymptotically Anti-de Sitter space. A central
aspect of our model is to consider a shell moving at finite velocity as
determined by its equation of motion, rather than a quasi-static approximation
as considered previously in the literature. By applying a divergence matching
method, we obtain the evolution of singularities in the retarded unequal time
correlator , which probes different stages of the thermalization. We
find that the number of singularities decreases from a finite number to zero as
the gauge theory thermalizes. This may be interpreted as a sign of decoherence.
Moreover, in a second part of the paper, we show explicitly that the thermal
correlator is characterized by the existence of singularities in the complex
time plane. By studying a quasi-static state, we show the singularities at real
times originate from contributions of normal modes. We also investigate the
possibility of obtaining complex singularities from contributions of
quasi-normal modes.Comment: 35 pages, 4 figure
Fast Scramblers, Horizons and Expander Graphs
We propose that local quantum systems defined on expander graphs provide a
simple microscopic model for thermalization on quantum horizons. Such systems
are automatically fast scramblers and are motivated from the membrane paradigm
by a conformal transformation to the so-called optical metric.Comment: 22 pages, 2 figures. Added further discussion in section 3. Added
reference
Time singularities of correlators from Dirichlet conditions in AdS/CFT
Within AdS/CFT, we establish a general procedure for obtaining the leading
singularity of two-point correlators involving operator insertions at different
times. The procedure obtained is applied to operators dual to a scalar field
which satisfies Dirichlet boundary conditions on an arbitrary time-like surface
in the bulk. We determine how the Dirichlet boundary conditions influence the
singularity structure of the field theory correlation functions. New
singularities appear at boundary points connected by null geodesics bouncing
between the Dirichlet surface and the boundary. We propose that their
appearance can be interpreted as due to a non-local double trace deformation of
the dual field theory, in which the two insertions of the operator are
separated in time. The procedure developed in this paper provides a technical
tool which may prove useful in view of describing holographic thermalization
using gravitational collapse in AdS space.Comment: 30 pages, 3 figures. Version as in JHE
Holographic Geometry of Entanglement Renormalization in Quantum Field Theories
We study a conjectured connection between the AdS/CFT and a real-space
quantum renormalization group scheme, the multi-scale entanglement
renormalization ansatz (MERA). By making a close contact with the holographic
formula of the entanglement entropy, we propose a general definition of the
metric in the MERA in the extra holographic direction, which is formulated
purely in terms of quantum field theoretical data. Using the continuum version
of the MERA (cMERA), we calculate this emergent holographic metric explicitly
for free scalar boson and free fermions theories, and check that the metric so
computed has the properties expected from AdS/CFT. We also discuss the cMERA in
a time-dependent background induced by quantum quench and estimate its
corresponding metric.Comment: 42pages, 9figures, reference added, minor chang
On Field Theory Thermalization from Gravitational Collapse
Motivated by its field theory interpretation, we study gravitational collapse
of a minimally coupled massless scalar field in Einstein gravity with a
negative cosmological constant. After demonstrating the accuracy of the
numerical algorithm for the questions we are interested in, we investigate
various aspects of the apparent horizon formation. In particular, we study the
time and radius of the apparent horizon formed as functions of the initial
Gaussian profile for the scalar field. We comment on several aspects of the
dual field theory picture.Comment: 31 pages, 17 figures; V2 Some figures corrected, minor revision.
arXiv admin note: substantial text overlap with arXiv:1106.233
Holographic Evolution of Entanglement Entropy
We study the evolution of entanglement entropy in a 2-dimensional
equilibration process that has a holographic description in terms of a Vaidya
geometry. It models a unitary evolution in which the field theory starts in a
pure state, its vacuum, and undergoes a perturbation that brings it far from
equilibrium. The entanglement entropy in this set up provides a measurement of
the quantum entanglement in the system. Using holographic techniques we recover
the same result obtained before from the study of processes triggered by a
sudden change in a parameter of the hamiltonian, known as quantum quenches.
Namely, entanglement in 2-dimensional conformal field theories propagates with
velocity v^2=1. Both in quantum quenches and in the Vaidya model equilibration
is only achieved at the local level. Remarkably, the holographic derivation of
this last fact requires information from behind the apparent horizon generated
in the process of gravitational collapse described by the Vaidya geometry. In
the early stages of the evolution the apparent horizon seems however to play no
relevant role with regard to the entanglement entropy. We speculate on the
possibility of deriving a thermalization time for occupation numbers from our
analysis.Comment: 26 pages, 10 figure
Gravitational collapse and thermalization in the hard wall model
We study a simple example of holographic thermalization in a confining field
theory: the homogeneous injection of energy in the hard wall model. Working in
an amplitude expansion, we find black brane formation for sufficiently fast
energy injection and a scattering wave solution for sufficiently slow
injection. We comment on our expectations for more sophisticated holographic
QCD models.Comment: 33 pages, 5 figure
Plasma photoemission from string theory
Leading 't Hooft coupling corrections to the photoemission rate of the planar
limit of a strongly-coupled {\cal {N}}=4 SYM plasma are investigated using the
gauge/string duality. We consider the full order \alpha'^3 type IIB string
theory corrections to the supergravity action, including higher order terms
with the Ramond-Ramond five-form field strength. We extend our previous results
presented in arXiv:1110.0526. Photoemission rates depend on the 't Hooft
coupling, and their curves suggest an interpolating behaviour from strong
towards weak coupling regimes. Their slopes at zero light-like momentum give
the electrical conductivity as a function of the 't Hooft coupling, in full
agreement with our previous results of arXiv:1108.6306. Furthermore, we also
study the effect of corrections beyond the large N limit.Comment: 36 pages, 5 figures, paragraph added in the conclusions, references
added, typos correcte
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