Partition Functions of Three-Dimensional Pure Gravity

TL;DR

This paper computes the partition function of three-dimensional pure gravity with negative cosmological constant by summing over gravitational instantons, proposing an exact formula for handlebody contributions across all genera and providing evidence at genus two.

Contribution

It introduces a conjectured exact expression for handlebody contributions to the ECFT partition function for all genera and values of k, supported by evidence at genus two.

Findings

Proposes an exact formula for handlebody contributions to the partition function.

Provides evidence supporting the conjecture at genus two.

Advances understanding of the duality between 3D gravity and ECFT.

Abstract

The three-dimensional pure quantum gravity with a negative cosmological constant has been conjectured to be dual to an extremal conformal field theory (ECFT), of central charge c=24k for some positive integer k. We compute the partition function of the dual ECFT by summing over gravitational instanton contributions. In particular, we conjecture an exact expression for the contribution from handlebodies to the partition function for all genera and all values of k, and provide nontrivial evidences for the conjecture at genus two.