One-loop partition function of three-dimensional flat gravity

TL;DR

This work analyzes the one-loop partition function of three-dimensional flat gravity and shows it naturally organizes into a representation of the $BMS_3$ asymptotic symmetry group. By performing a heat-kernel evaluation on the thermal quotient of flat space and using the method of images, the authors derive an explicit one-loop correction and demonstrate that the total partition function matches the vacuum $BMS_3$ character with central charge $c_2=3/G$, consistent with the flat limit of the AdS$_3$ result. The approach argues that the perturbative quantum gravity in flat space has its states described by coadjoint orbits of $BMS_3$, yielding one-loop exact results with higher-loop corrections vanishing. This work provides a concrete quantum check of the $BMS_3$ structure in flat-space holography and clarifies the link between bulk gravity and $BMS_3$ representation theory.

Abstract

In this note we point out that the one-loop partition function of three-dimensional flat gravity, computed along the lines originally developed for the anti-de Sitter case, reproduces characters of the BMS3 group.