Quantum Corrections to Bekenstein-Hawking Black Hole Entropy and Gravity Partition Functions

TL;DR

This paper analyzes quantum corrections to black hole entropy in AdS_3, using algebraic and conformal field theory methods, and presents a systematic way to include these corrections via spectral functions and Virasoro modules.

Contribution

It introduces a spectral function approach to systematically incorporate quantum corrections to black hole entropy and partition functions in AdS_3/CFT_2.

Findings

Quantum corrections can be expressed using Patterson-Selberg spectral functions.

Partition functions are related to Virasoro module characters.

A holomorphic factorization of quantum contributions is achieved.

Abstract

Algebraic aspects of the computation of partition functions for quantum gravity and black holes in $AdS_3$ are discussed. We compute the sub-leading quantum corrections to the Bekenstein-Hawking entropy. It is shown that the quantum corrections to the classical result can be included systematically by making use of the comparison with conformal field theory partition functions, via the $AdS_3/CFT_2$ correspondence. This leads to a better understanding of the role of modular and spectral functions, from the point of view of the representation theory of infinite-dimensional Lie algebras. Besides, the sum of known quantum contributions to the partition function can be presented in a closed form, involving the Patterson-Selberg spectral function. These contributions can be reproduced in a holomorphically factorized theory whose partition functions are associated with the formal characters of the Virasoro modules. We propose a spectral function formulation for quantum corrections to the elliptic genus from supergravity states.