BMS$_3$ fermionic localization

TL;DR

This paper applies fermionic localization to compute the exact torus partition function of 3d pure gravity with BMS$_3$ symmetry, demonstrating its 1-loop exactness and providing insights into quantum aspects of flat space holography.

Contribution

It introduces a fermionic localization method to evaluate the partition function in BMS$_3$ gravity, a novel approach in this context.

Findings

Exact torus partition function computed for BMS$_3$ symmetry

Demonstration of 1-loop exactness of the partition function

Insights into quantum properties of 3d flat space gravity

Abstract

We consider the geometric action formulation for 3d pure gravity with vanishing cosmological constant. We use fermionic localization to compute the exact torus partition function for a constant representative coadjoint orbit of $\widehat{\text{BMS}}_3$. This allows us to discuss its 1-loop exactness.