Partition Functions of Three-Dimensional Quantum Gravity and the Black Hole Entropy

TL;DR

This paper explores the quantum gravity partition functions in AdS3, revealing exact formulations involving the Patterson-Selberg zeta function and their implications for black hole entropy within the holographic framework.

Contribution

It provides an exact expression for the quantum gravity partition functions in AdS3, including corrections, using the Patterson-Selberg zeta function, advancing understanding of holography and black hole entropy.

Findings

Exact partition function expressions involving Patterson-Selberg zeta function

Inclusion of corrections to known partition functions

Insights into holographic principles and black hole entropy

Abstract

We analyze aspects of the holographic principle relevant to the quantum gravity partition functions in Euclidean sector of AdS$_3$. The sum of the known contributions to the partitions functions can be presented exactly, including corrections, in the form where the Patterson-Selberg zeta function involves.