118496902
Note on thermodynamics method of black hole/CFT correspondence
A bstractIn 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 S+S− 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 T+A+ = T−A−, with A± 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 T+A+ = T−A− is just the condition T+S+ = T−S−, with S± being the outer and inner horizon entropies, which is the condition for the entropy product S+S− 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.
119261249
General hidden conformal symmetry of 4D Kerr-Newman and 5D Kerr black holes
There are two known CFT duals, namely the J-picture and the Q-picture, for a four-dimensional Kerr-Newman black hole, corresponding to the angular momentum J and the electric charge Q respectively. In our recent study we found a one-parameter class of CFT duals for extremal Kerr-Newman black hole, connecting these two pictures. In this paper we study these novel CFT duals for the generic non-extremal Kerr-Newman black hole. We investigate the hidden conformal symmetry in the low frequency scattering off Kerr-Newman black hole, from which the dual temperatures could be read. We find that there still exists a hidden conformal symmetry for a general CFT dual. We reproduce the correct Bekenstein-Hawking entropy from the Cardy formula, assuming the form of the central charge being invariant. Moreover we compute the retarded Green’s function in the general CFT dual picture and find it is in good match with the CFT prediction. Furthermore we discuss the hidden conformal symmetries of the five dimensional Kerr black hole and obtain the similar evidence to support the general dual CFT pictures.
118664541
Quasi-normal modes of extremal black holes from hidden conformal symmetry
In this Letter, we construct the quasi-normal modes of three-dimensional extremal black holes in an algebraic way. We show that the infinite towers of the quasi-normal modes of scalar, vector and tensor could be constructed as the descendents of the highest weight modes. Our investigation shows that the hidden conformal symmetry suggested in Chen et al. (2010) [5] is an intrinsic property of the extremal black hole. Moreover, we notice that we need to fix the freedom in defining the local vector fields and find the right hidden conformal symmetry to obtain the physical quasi-normal modes. (C) 2011 Elsevier B.V. All rights reserved.
118388512
Note on generalized gravitational entropy in Lovelock gravity
A bstractThe recently proposed gravitational entropy generalize the usual black hole entropy to Euclidean solutions without U(1) symmetry in the framework of Einstein gravity. The entropy of such smooth configuration is given by the area of minimal surface, therefore explaining the Ryu-Takayanagi formula of holographic entanglement entropy. In this note we investigate the generalized gravitational entropy for general Lovelock gravity in arbitrary dimensions. We use the replica trick and consider the Euclidean bulk spacetime with conical singularity localized at a codimension two surface. We obtain a constraint equation for the surface by requiring the bulk equation of motion to be of good behavior. When the bulk spacetime is maximally symmetric, the constraints show that the traces of the extrinsic curvatures of the surface are vanishing, i.e. the surface has to be geometrically a minimal surface. However the constraint equation cannot be obtained by the variation of the known functional for holographic entanglement entropy in Lovelock gravity.
119259850
RN/CFT correspondence from thermodynamics
A bstractRecent 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-Nordström (RN) black holes in arbitrary dimensions by using the thermodynamics method.We refine the thermodynamics method proposed in [20] 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 SL(2, Z) transformations.
118385893
On short interval expansion of Rényi entropy
A bstractRényi entanglement entropy provides a new window to study the AdS/CFT correspondence. In this paper we consider the short interval expansion of Rényi 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 Rényi 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 Rényi entropy. In the case of two short disjoint intervals with a small cross ratio x, we obtain not only the classical and 1-loop quantum contributions to the Rényi entropy to order x6, both of which are in perfect match with the ones found in gravity, but also the leading 1/c contributions, which corresponds to 2-loop corrections in the bulk.
17145116
Nonperturbative renormalization of composite operators with overlap fermions
We compute nonperturbatively the renormalization constants of composite operators on a quenched 16{sup 3}x28 lattice with lattice spacing a=0.20 fm for the overlap fermion by using the regularization-independent (RI) scheme. The quenched gauge configurations were generated with the Iwasaki action. We test the relations Z{sub A}=Z{sub V} and Z{sub S}=Z{sub P} and find that they agree well (less than 1%) above {mu}=1.6 GeV. We also perform a Renormalization Group (RG) analysis at the next-to-next-to-leading order and match the renormalization constants to the MS scheme. The wave function renormalization Z{sub {psi}} is determined from the vertex function of the axial current and Z{sub A} from the chiral Ward identity. Finally, we examine the finite quark mass behavior for the renormalization factors of the quark bilinear operators. We find that the (pa){sup 2} errors of the vertex functions are small and the quark mass dependence of the renormalization factors to be quite weak.
118538162
Hydrodynamics of a 5D Einstein-dilaton black hole solution and the corresponding BPS state
A bstractWe apply the potential reconstruction approach to generate a series of asymp-totically AdS (aAdS) black hole solutions, with a self-interacting bulk scalar field. Based on the method, we reproduce the pure AdS solution as a consistency check and we also generate a simple analytic 5D black hole solution. We then study various aspects of this solution, such as temperature, entropy density and conserved charges. Furthermore, we study the hydrodynamics of this black hole solution in the framework of fluid/gravity duality, e.g. the ratio of the shear viscosity to the entropy density. In a degenerate case of the 5D black hole solution, we find that the c function decreases monotonically from UV to IR as expected. Finally, we investigate the stability of the degenerate solution by studying the bosonic functional energy of the gravity and the Witten-Nester energy EWN. We confirm that the degenerate solution is a BPS domain wall solution. The corresponding superpotential and the solution of the killing spinor equation are found explicitly.
118483519
Hydrodynamics with conserved current via AdS/CFT correspondence in the Maxwell-Gauss-Bonnet gravity
Using the AdS/CFT correspondence, we study the hydrodynamics with conserved current from the dual Maxwell-Gauss-Bonnet gravity. After constructing the perturbative solution to the first order based on the boosted black brane solution in the bulk Maxwell-Gauss-Bonnet gravity, we extract the stress tensor and conserved current of the dual conformal fluid on its boundary, and also find the effect of Gauss-Bonnet term on the dual conformal fluid. Our results show that the Gauss-Bonnet term can affect the parameters such as the shear viscosity $\eta$, entropy density $s$, thermal conductivity $\kappa$ and electrical conductivity $\sigma$. However, it does not affect the so-called Wiedemann-Franz law which relates $\kappa$ to $\sigma$, while it affects the ratio $\eta/s$. In addition, another interesting result is that the $\eta/s$ can also be affected by the bulk Maxwell field in our case, which is consistent with some previous results predicted through the Kubo formula. Moreover, the anomalous magnetic and vortical effects by adding the Chern-Simons term are also considered in our case in the Maxwell-Gauss-Bonnet gravity.
119452670
Pion decay constant, ZA and chiral log from overlap fermions
Abstract We report our calculation of the pion decay constant f π , the axial renormalization constant Z A , and the quenched chiral logarithms from the overlap fermions. The calculation is done on a quenched 20 4 lattice at a = 0.148 fm using tree level tadpole improved gauge action. The smallest pion mass we reach is about 280 MeV. The lattice size is about 4 times the Compton wavelength of the lowest mass pion.
118580324
Proliferation of the Phoenix Universe
Cyclic cosmology, in which the universe will experience alternating periods of gravitational collapse and expansion, provides an interesting understanding of the early universe and is described as "The Phoenix Universe". In usual expectation, the cyclic universe should be homogeneous, however, with studying the cosmological perturbations, we find that the amplification of curvature perturbations on the large scale may rip the homogeneous universe into a fissiparous multiverse after one or several cycles. Thus, we suggest that the cyclic universe not only rebirths in the "fire" and will never ended, like the Phoenix, but also proliferates eternally.