Black hole microstate counting and its macroscopic counterpart

We develop new techniques to efficiently evaluate heat kernel coefficients for the Laplacian in the short-time expansion on spheres and hyperboloids with conical singularities. We then apply these techniques to explicitly compute the logarithmic contribution to black hole entropy from an N = 4 vector multiplet about a Z N orbifold of the nearhorizon geometry of quarter-BPS black holes in N = 4 supergravity. We find that this vanishes, matching perfectly with the prediction from the microstate counting. We also discuss possible generalisations of our heat kernel results to higher-spin fields over Z N orbifolds of higher-dimensional spheres and hyperboloids.

Section: Jhep03(2014)043mentioning

confidence: 99%

Section: Jhep03(2014)043 1 Introductionmentioning

confidence: 99%

Heat kernels on the AdS2 cone and logarithmic corrections to extremal black hole entropy

Gupta

Lal

Thakur

2014

“…That is, we wish to turn the behavior (sinh η) ∆−1 off entirely. 5 Using the result (A.8) from appendix A, this is accomplished whenever ∆ = ∆ ⋆ where…”

Section: Finding the Zero Modesmentioning

confidence: 99%

Partition functions in even dimensional AdS via quasinormal mode methods

Keeler

2014

In this note, we calculate the one-loop determinant for a massive scalar (with conformal dimension ∆) in even-dimensional AdS d+1 space, using the quasinormal mode method developed in [1] by Denef, Hartnoll, and Sachdev. Working first in two dimensions on the related Euclidean hyperbolic plane H 2 , we find a series of zero modes for negative real values of ∆ whose presence indicates a series of poles in the one-loop partition function Z(∆) in the ∆ complex plane; these poles contribute temperature-independent terms to the thermal AdS partition function computed in [1]. Our results match those in a series of papers by Camporesi and Higuchi, as well as Gopakumar et al. [2] and Banerjee et al. [3]. We additionally examine the meaning of these zero modes, finding that they Wick-rotate to quasinormal modes of the AdS 2 black hole. They are also interpretable as matrix elements of the discrete series representations of SO(2, 1) in the space of smooth functions on S 1 . We generalize our results to general even dimensional AdS 2n , again finding a series of zero modes which are related to discrete series representations of SO(2n, 1), the motion group of H 2n .

“…Recent discussions on the quantum black hole entropy of extremal black holes and the AdS 2 /CFT 1 correspondence suggest the identification of the black hole entropy with the logarithm of the string ground state degeneracy [8][9][10]. This is an integer, N , fixed by the set of the black hole's electric and magnetic charges.…”

Section: Jhep02(2014)109 3 Modular Discretization and Quantum Dynamicmentioning

confidence: 99%

“…We should stress here that recent developments in string theory [6][7][8][9][10], which take into account the correct definition of the black hole entropy at the quantum level, have improved considerably our understanding of the black hole microscopic degrees of freedom. We understand now some important quantum statistical properties, in particular, the exact quantum entropy, for a certain class of extremal black holes.…”

Section: Introductionmentioning

confidence: 99%

Modular discretization of the AdS2/CFT1 holography

Axenides

Floratos

Nicolis

2014

We propose a finite discretization for the black hole, near horizon, geometry and dynamics. We realize our proposal, in the case of extremal black holes, for which the radial and temporal near horizon geometry is known to be AdS 2 = SL(2, R)/SO(1, 1, R). We implement its discretization by replacing the set of real numbers R with the set of integers modulo N with AdS 2 going over to the finite geometry AdS 2 [N ] = SL(2, Z N )/SO(1, 1, Z N ). We model the dynamics of the microscopic degrees of freedom by generalized Arnol'd cat maps, A ∈ SL(2, Z N ) which are isometries of the geometry, at both the classical and quantum levels. These are well known to exhibit fast quantum information processing through the well studied properties of strong arithmetic chaos, dynamical entropy, nonlocality and factorization in the cutoff discretization N . We construct, finally, a new kind of unitary and holographic correspondence, for AdS 2 [N ]/CFT 1 [N ], via coherent states of the bulk and boundary geometries.