232 research outputs found
Time evolution of entanglement entropy from a pulse
We calculate the time evolution of the entanglement entropy in a 1+1 CFT with
a holographic dual when there is a localized left-moving packet of energy
density. We find the gravity result agrees with a field theory result derived
from the transformation properties of R\'enyi entropy. We are able to reproduce
behavior which qualitatively agrees with CFT results of entanglement entropy of
a system subjected to a local quench. In doing so we construct a finite
diffeomorphism which tales three-dimensional anti-de Sitter space in the
Poincar\'e patch to a general solution, generalizing the diffeomorphism that
takes the Poincar\'e patch a BTZ black hole. We briefly discuss the calculation
of correlation functions in these backgrounds and give results at large
operator dimension.Comment: 18 pages, 6 figure
Measuring Black Hole Formations by Entanglement Entropy via Coarse-Graining
We argue that the entanglement entropy offers us a useful coarse-grained
entropy in time-dependent AdS/CFT. We show that the total von-Neumann entropy
remains vanishing even when a black hole is created in a gravity dual, being
consistent with the fact that its corresponding CFT is described by a
time-dependent pure state. We analytically calculate the time evolution of
entanglement entropy for a free Dirac fermion on a circle following a quantum
quench. This is interpreted as a toy holographic dual of black hole creations
and annihilations. It is manifestly free from the black hole information
problem.Comment: 25 pages, Latex, 8 figure
Positivity, entanglement entropy, and minimal surfaces
The path integral representation for the Renyi entanglement entropies of
integer index n implies these information measures define operator correlation
functions in QFT. We analyze whether the limit , corresponding
to the entanglement entropy, can also be represented in terms of a path
integral with insertions on the region's boundary, at first order in .
This conjecture has been used in the literature in several occasions, and
specially in an attempt to prove the Ryu-Takayanagi holographic entanglement
entropy formula. We show it leads to conditional positivity of the entropy
correlation matrices, which is equivalent to an infinite series of polynomial
inequalities for the entropies in QFT or the areas of minimal surfaces
representing the entanglement entropy in the AdS-CFT context. We check these
inequalities in several examples. No counterexample is found in the few known
exact results for the entanglement entropy in QFT. The inequalities are also
remarkable satisfied for several classes of minimal surfaces but we find
counterexamples corresponding to more complicated geometries. We develop some
analytic tools to test the inequalities, and as a byproduct, we show that
positivity for the correlation functions is a local property when supplemented
with analyticity. We also review general aspects of positivity for large N
theories and Wilson loops in AdS-CFT.Comment: 36 pages, 10 figures. Changes in presentation and discussion of
Wilson loops. Conclusions regarding entanglement entropy unchange
Holographic Studies of Entanglement Entropy in Superconductors
We present the results of our studies of the entanglement entropy of a
superconducting system described holographically as a fully back-reacted
gravity system, with a stable ground state. We use the holographic prescription
for the entanglement entropy. We uncover the behavior of the entropy across the
superconducting phase transition, showing the reorganization of the degrees of
freedom of the system. We exhibit the behaviour of the entanglement entropy
from the superconducting transition all the way down to the ground state at
T=0. In some cases, we also observe a novel transition in the entanglement
entropy at intermediate temperatures, resulting from the detection of an
additional length scale.Comment: 21 pages, 14 figures. v2:Clarified some remarks concerning stability.
v3: Updated to the version that appears 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
Heavy quark density in N=4 SYM: from hedgehog to Lifshitz spacetimes
We study the effect of an order N^2 density of heavy quarks in strongly
coupled N=4 SUSY Yang-Mills theory in the large N limit. This is achieved in
the type IIB supergravity dual by introducing a uniformly smeared density of
macroscopic string sources stretching to the boundary of AdS_5 x S^5. The
backreacted system exhibits a flow from an AdS_5 "hedgehog" geometry to a
scaling Lifshitz-like solution Lif_5 x S^5 with dynamical critical exponent
z=7, wherein the scaling symmetry is broken by a logarithmic running dilaton.
We find an exact black brane solution within the scaling regime which describes
the low temperature thermodynamics of the system.Comment: 20 pages, 2 figures, references adde
Thermal phases of D1-branes on a circle from lattice super Yang-Mills
We report on the results of numerical simulations of 1+1 dimensional SU(N)
Yang-Mills theory with maximal supersymmetry at finite temperature and
compactified on a circle. For large N this system is thought to provide a dual
description of the decoupling limit of N coincident D1-branes on a circle. It
has been proposed that at large N there is a phase transition at strong
coupling related to the Gregory-Laflamme (GL) phase transition in the
holographic gravity dual. In a high temperature limit there was argued to be a
deconfinement transition associated to the spatial Polyakov loop, and it has
been proposed that this is the continuation of the strong coupling GL
transition. Investigating the theory on the lattice for SU(3) and SU(4) and
studying the time and space Polyakov loops we find evidence supporting this. In
particular at strong coupling we see the transition has the parametric
dependence on coupling predicted by gravity. We estimate the GL phase
transition temperature from the lattice data which, interestingly, is not yet
known directly in the gravity dual. Fine tuning in the lattice theory is
avoided by the use of a lattice action with exact supersymmetry.Comment: 21 pages, 8 figures. v2: References added, two figures were modified
for clarity. v3: Normalisation of lattice coupling corrected by factor of two
resulting in change of estimate for c_cri
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