5,907 research outputs found
Thermodynamics of two-dimensional conformal field theory dual to black holes
In this note we investigate the first law of thermodynamics of the
two-dimensional conformal field theory (CFT) that is dual to black holes. We
start from the Cardy formula and get the CFT thermodynamics with minimal
reasonable assumptions. We use both the microcanonical ensemble and canonical
ensemble versions of the Cardy formula. In the black hole/CFT correspondence
the black hole is dual to a CFT with excitations, and the black hole mass
and charge correspond to the energy and charge of the excited CFT. The CFT
left- and right-moving central charges should be quantized, and so we
assume that they are mass-independent. Also we assume the difference of the
left- and right-moving sector levels is mass-independent dual to
level matching condition. The thermodynamics of two-dimensional CFT we get is
universal and supports the thermodynamics method of black hole/CFT
correspondence.Comment: 10 page
On short interval expansion of R\'enyi entropy
R\'enyi entanglement entropy provides a new window to study the AdS/CFT
correspondence. In this paper we consider the short interval expansion of
R\'enyi entanglement entropy in two-dimensional conformal field theory. This
amounts to do the operator product expansion of the twist operators. We focus
on the vacuum Verma module and consider the quasiprimary operators constructed
from the stress tensors. After obtaining the expansion coefficients of the
twist operators to level 6 in vacuum Verma module, we compute the leading
contributions to the R\'enyi entropy, to order 6 in the short interval
expansion. In the case of one short interval on cylinder, we reproduce the
first several leading contributions to the R\'enyi entropy. In the case of two
short disjoint intervals with a small cross ratio , we obtain not only the
classical and 1-loop quantum contributions to the R\'enyi entropy to order
, both of which are in perfect match with the ones found in gravity, but
also the leading contributions, which corresponds to 2-loop corrections
in the bulk.Comment: V1, 23 pages, 5 figures; V2, published version, typos corrected,
references adde
Thermodynamics in Black-hole/CFT Correspondence
The area law of Bekenstein-Hawking entropy of the black hole suggests that
the black hole should have a lower-dimensional holographic description. It has
been found recently that a large class of rotating and charged black holes
could be holographically described a two-dimensional (2D) conformal field
theory (CFT). We show that the universal information of the dual CFT, including
the central charges and the temperatures, is fully encoded in the
thermodynamics laws of both outer and inner horizons. These laws,
characterizing how the black hole responds under the perturbation, allows us to
read different dual pictures with respect to different kinds of perturbations.
The remarkable effectiveness of this thermodynamics method suggest that the
inner horizon could play a key role in the study of holographic description of
the black hole.Comment: 8 pages. Essay awarded honourable mention in the Gravity Research
Foundation 2013 Awards for Essays on Gravitatio
RN/CFT Correspondence From Thermodynamics
Recent studies suggest that in the Kerr/CFT correspondence, much universal
information of the dual CFT, including the central charges and the
temperatures, is fully encoded in the thermodynamics of the outer and inner
horizons of the Kerr(-Newman) black holes. In this paper, we study holographic
descriptions of Reissner-Nordstr\"om (RN) black holes in arbitrary dimensions
by using the thermodynamics method.We refine the thermodynamics method proposed
in arXiv:1206.2015 by imposing the "quantization" condition so that we can fix
the ambiguity in determining the central charges of the dual CFT of RN black
holes. Using the refined thermodynamics method, we find the holographic CFT
duals for the RN black holes, and confirm these pictures by using conventional
analysis of asymptotic symmetry group and the hidden conformal symmetry in the
low-frequency scattering. In particular, we revisit the four-dimensional dyonic
RN black hole and find a novel magnetic picture, besides the known electric CFT
dual picture. We show how to generate a class of dual dyonic pictures by
transformations.Comment: 32 pages, references added, published versio
Quasinormal Modes and Hidden Conformal Symmetry of Warped dS Black Hole
In this paper, we analytically calculate the quasinormal modes of scalar,
vector, tensor, and spinor perturbations of the warped dS black hole. There
are two horizons for the warped dS black hole, namely, the black hole
horizon and the cosmological horizon . In the calculation, we impose
the ingoing boundary condition at the black hole horizon and the outgoing
boundary condition at the cosmological horizon. We also investigate the hidden
conformal symmetry of the warped dS black hole in the region between the
black hole horizon and the cosmological horizon . We use the hidden
conformal symmetry to construct the quasinormal modes in an algebraic way and
find that the results agree with the analytically ones. It turns out that the
frequencies of the quasinormal modes could be identified with the poles in the
thermal boundary-boundary correlators.Comment: 26 pages, references added, published versio
Note on Thermodynamics Method of Black Hole/CFT Correspondence
In the paper we further refine the thermodynamics method of black hole/CFT
correspondence. We show that one can derive the central charges of different
holographic pictures directly from the entropy product if it is
mass-independent, for a black hole in the Einstein gravity or the gravity
without diffeomorphism anomaly. For a general black hole in the Einstein
gravity that admits holographic descriptions, we show that the thermodynamics
method and asymptotic symmetry group (ASG) analysis can always give consistent
results in the extreme limit. Furthermore, we discuss the relation between
black hole thermodynamics and the hidden conformal symmetry. We show that the
condition , with being the outer and inner horizon
areas, is the necessary, but not sufficient, condition for a black hole to have
the hidden conformal symmetry. In particular, for the Einstein(-Maxwell)
gravity is just the condition , with
being the outer and inner horizon entropies, which is the condition for the
entropy product being mass-dependent. When there exists the hidden
conformal symmetry in the low-frequency scattering off the generic non-extremal
black hole, it always leads to the same temperatures of dual CFT as the ones
got from the thermodynamics method.Comment: 31 pages, references added, published versio
- β¦