204 research outputs found
Holographic reconstruction of spacetime and renormalization in the AdS/CFT correspondence
We develop a systematic method for renormalizing the AdS/CFT prescription for
computing correlation functions. This involves regularizing the bulk on-shell
supergravity action in a covariant way, computing all divergences, adding
counterterms to cancel them and then removing the regulator. We explicitly work
out the case of pure gravity up to six dimensions and of gravity coupled to
scalars. The method can also be viewed as providing a holographic
reconstruction of the bulk spacetime metric and of bulk fields on this
spacetime, out of conformal field theory data. Knowing which sources are turned
on is sufficient in order to obtain an asymptotic expansion of the bulk metric
and of bulk fields near the boundary to high enough order so that all infrared
divergences of the on-shell action are obtained. To continue the holographic
reconstruction of the bulk fields one needs new CFT data: the expectation value
of the dual operator. In particular, in order to obtain the bulk metric one
needs to know the expectation value of stress-energy tensor of the boundary
theory. We provide completely explicit formulae for the holographic
stress-energy tensors up to six dimensions. We show that both the gravitational
and matter conformal anomalies of the boundary theory are correctly reproduced.
We also obtain the conformal transformation properties of the boundary
stress-energy tensors
Entanglement Entropy in Non-Relativistic Field Theories
We calculate entanglement entropy in a non-relativistic field theory
described by the Schr\"odinger operator. We demonstrate that the entropy is
characterized by i) the area law and ii) UV divergences that are identical to
those in the relativistic field theory. These observations are further
supported by a holographic consideration. We use the non-relativistic symmetry
and completely specify entanglement entropy in large class of non-relativistic
theories described by the field operators polynomial in derivatives. We suggest
that the area law of the entropy can be tested in experiments with condensed
matter systems such as liquid helium.Comment: 4 pages; v2: discussion of interacting fields include
Remarks on effective action and entanglement entropy of Maxwell field in generic gauge
We analyze the dependence of the effective action and the entanglement
entropy in the Maxwell theory on the gauge fixing parameter in
dimensions. For a generic value of the corresponding vector operator is
nonminimal. The operator can be diagonalized in terms of the transverse and
longitudinal modes. Using this factorization we obtain an expression for the
heat kernel coefficients of the nonminimal operator in terms of the
coefficients of two minimal Beltrami-Laplace operators acting on 0- and
1-forms. This expression agrees with an earlier result by Gilkey et al. Working
in a regularization scheme with the dimensionful UV regulators we introduce
three different regulators: for transverse, longitudinal and ghost modes,
respectively. We then show that the effective action and the entanglement
entropy do not depend on the gauge fixing parameter provided the certain
(-dependent) relations are imposed on the regulators. Comparing the
entanglement entropy with the black hole entropy expressed in terms of the
induced Newton's constant we conclude that their difference, the so-called
Kabat's contact term, does not depend on the gauge fixing parameter . We
consider this as an indication of gauge invariance of the contact term.Comment: 15 pages; v2: typos in eqs. (31), (32), (34), (36) corrected;
discussion in section 6 expande
Heat Kernel Expansion and Extremal Kerr-Newmann Black Hole Entropy in Einstein-Maxwell Theory
We compute the second Seely-DeWitt coefficient of the kinetic operator of the
metric and gauge fields in Einstein-Maxwell theory in an arbitrary background
field configuration. We then use this result to compute the logarithmic
correction to the entropy of an extremal Kerr-Newmann black hole.Comment: 12 page
Logarithmic Corrections to Schwarzschild and Other Non-extremal Black Hole Entropy in Different Dimensions
Euclidean gravity method has been successful in computing logarithmic
corrections to extremal black hole entropy in terms of low energy data, and
gives results in perfect agreement with the microscopic results in string
theory. Motivated by this success we apply Euclidean gravity to compute
logarithmic corrections to the entropy of various non-extremal black holes in
different dimensions, taking special care of integration over the zero modes
and keeping track of the ensemble in which the computation is done. These
results provide strong constraint on any ultraviolet completion of the theory
if the latter is able to give an independent computation of the entropy of
non-extremal black holes from microscopic description. For Schwarzschild black
holes in four space-time dimensions the macroscopic result seems to disagree
with the existing result in loop quantum gravity.Comment: LaTeX, 40 pages; corrected small typos and added reference
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
Gravitational Chern-Simons Lagrangians and black hole entropy
We analyze the problem of defining the black hole entropy when Chern-Simons
terms are present in the action. Extending previous works, we define a general
procedure, valid in any odd dimensions both for purely gravitational CS terms
and for mixed gauge-gravitational ones. The final formula is very similar to
Wald's original formula valid for covariant actions, with a significant
modification. Notwithstanding an apparent violation of covariance we argue that
the entropy formula is indeed covariant.Comment: 39 page
Black Holes in Gravity with Conformal Anomaly and Logarithmic Term in Black Hole Entropy
We present a class of exact analytic and static, spherically symmetric black
hole solutions in the semi-classical Einstein equations with Weyl anomaly. The
solutions have two branches, one is asymptotically flat and the other
asymptotically de Sitter. We study thermodynamic properties of the black hole
solutions and find that there exists a logarithmic correction to the well-known
Bekenstein-Hawking area entropy. The logarithmic term might come from non-local
terms in the effective action of gravity theories. The appearance of the
logarithmic term in the gravity side is quite important in the sense that with
this term one is able to compare black hole entropy up to the subleading order,
in the gravity side and in the microscopic statistical interpretation side.Comment: Revtex, 10 pages. v2: minor changes and to appear in JHE
Entanglement Entropy of Two Spheres
We study the entanglement entropy S_{AB} of a massless free scalar field on
two spheres A and B whose radii are R_1 and R_2, respectively, and the distance
between the centers of them is r. The state of the massless free scalar field
is the vacuum state. We obtain the result that the mutual information
S_{A;B}:=S_A+S_B-S_{AB} is independent of the ultraviolet cutoff and
proportional to the product of the areas of the two spheres when r>>R_1,R_2,
where S_A and S_B are the entanglement entropy on the inside region of A and B,
respectively. We discuss possible connections of this result with the physics
of black holes.Comment: 17 pages, 9 figures; v4, added references, revised argument in
section V, a typo in eq.(25) corrected, published versio
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
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