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.
119188234
Notes on Self-dual Warped dS$_3$ Spacetime
In this paper, we investigate the warped dS/CFT correspondence of the self-dual warped dS$_3$ spacetime, which is a solution of three-dimensional topologically massive gravity (TMG) with a positive cosmological constant. We discuss its thermodynamics at two cosmological horizons. We propose that the self-dual warped dS$_3$ spacetime is holographically dual to a chiral conformal field theory. We analytically calculate the quasinormal modes of scalar, vector, tensor, and spinor perturbations under the self-dual warped dS$_3$ spacetime. It turns out that the frequencies of the quasinormal modes could be identified with the poles in the thermal boundary-boundary correlators.
118607645
Hidden conformal symmetry of extremal black holes
We study the hidden conformal symmetry of extremal black holes. We introduce a new set of conformal coordinates to write the SL(2,R) generators. We find that the Laplacian of the scalar field in many extremal black holes, including Kerr(-Newman), Reissner-Nordstrom, warped AdS{sub 3}, and null warped black holes, could be written in terms of the SL(2,R) quadratic Casimir. This suggests that there exist dual conformal field theory (CFT) descriptions of these black holes. From the conformal coordinates, the temperatures of the dual CFTs could be read directly. For the extremal black hole, the Hawking temperature is vanishing. Correspondingly, only the left (right) temperature of the dual CFT is nonvanishing, and the excitations of the other sector are suppressed. In the probe limit, we compute the scattering amplitudes of the scalar off the extremal black holes and find perfect agreement with the CFT prediction.
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.
118593197
Holographic descriptions of black rings
A bstractIn this paper, we investigate the holographic descriptions of two kinds of black rings, the neutral doubly rotating black ring and the dipole charged black ring. For generic nonextremal black rings, the information of holographic CFT duals, including the central charges and left- and right-moving temperatures, could be read from the thermodynamics at the outer and inner horizons, as suggested in [20]. To confirm these pictures, we study the extreme black rings in the well-established formalism. We compute the central charges of dual CFTs by doing asymptotic symmetry group analysis in the stretched horizon formalism, and find exact agreements. Moreover, we study the superradiant scattering of a scalar field off the near-extremal black rings and obtain the scattering amplitudes, which are in good match with the CFT predictions.
118544209
Holographic Rényi entropy for CFT with W symmetry
A bstractIn this paper we investigate the holographic Rényi entropy of two disjoint intervals on complex plane with small cross ratio x for conformal field theory with W symmetry in the ground state, which could be dual to a higher spin AdS3 gravity. We focus on the cases of W3 and W4 symmetries. In order to see the nontrivial contributions from the W fields, we calculate the Rényi entropy in the expansion of x to order x8 in both the gravity and the CFT sides. In the gravity side the classical contributions to the entanglement entropy is still given by the Ryu-Takayanagi area formula under the reasonable assumption, while the 1-loop quantum corrections have to take into account of the contributions not only from massless gravitons, but also from massless higher spin fields. In the CFT side we still use the operator product expansion of twist operators in the small interval limit, but now we need to consider the quasiprimary fields constructed from W fields, besides the ones from Virasoro Verma module. In the large central charge limit, we obtain the classical, 1-loop, 2-loop, and 3-loop parts of the Rényi entropy. The classical and 1-loop results in the gravity and the CFT sides are in exact match. This confirms the higher spin gravity/CFT correspondence, and also supports the holographic computation of Rényi entanglement entropy, including the quantum correction, in both the AdS3 gravity and the higher spin AdS3 gravity.
119297105
On the two-loop hexagon Wilson loop remainder function in N=4 SYM
Abstract A duality relation has been proposed between the planar gluon MHV amplitudes and light-like Wilson loops in N = 4 super Yang–Mills. At six-point two-loop, the results for the planar gluon MHV amplitude and for the light-like Wilson loop agree, but they both differ from the Bern–Dixon–Smirnov ansatz by a finite remainder function. Recently Del Duca, Duhr and Smirnov presented an analytical result for the two-loop hexagon Wilson loop remainder function in general kinematics. Their result is rather lengthy, and the dependence on the conformal cross ratios appears in a complicated way. Here we present an alternate, more compact representation for the two-loop hexagon Wilson loop remainder function.
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.
45784849
Past incompleteness of a bouncing multiverse
According to classical GR, Anti-de Sitter (AdS) bubbles in the multiverse terminate in big crunch singularities. It has been conjectured, however, that the fundamental theory may resolve these singularities and replace them by nonsingular bounces. This may have important implications for the beginning of the multiverse. Geodesics in cosmological spacetimes are known to be past-incomplete, as long as the average expansion rate along the geodesic is positive, but it is not clear that the latter condition is satisfied if the geodesic repeatedly passes through crunching AdS bubbles. We investigate this issue in a simple multiverse model, where the spacetime consists of a patchwork of FRW regions. The conclusion is that the spacetime is still past-incomplete, even in the presence of AdS bounces.
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.
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.