The massive BMS character in 3D quantum gravity

TL;DR

This paper derives the one-loop partition function for 3D quantum gravity with a conical defect, revealing how massive BMS$_3$ particles emerge from symmetry breaking, using both discrete and continuum geometric methods.

Contribution

It provides a novel derivation of the massive BMS$_3$ character in quantum gravity, linking defect-induced symmetry breaking to the emergence of massive modes through discrete and continuum frameworks.

Findings

Massive BMS$_3$ character derived from quantum gravity with defects

Consistency shown between discrete Regge and continuum boundary approaches

Diffeomorphism breaking by defects explains massive mode emergence

Abstract

We derive the one-loop partition function for three-dimensional quantum gravity in a finite-radius thermal twisted flat space with a conical defect, reproducing the massive BMS$_3$ character. We perform the computation in both discrete and continuum geometry formulations, showing consistency between them. In the discrete case, we integrate out bulk degrees of freedom in a Regge gravity framework, while in the continuum, we construct a dual non-local boundary field theory encoding geodesic length fluctuations. Our study shows that the additional modes of the massive character, compared to the vacuum case, originate from the explicit breaking of radial diffeomorphism symmetry by the defect. This provides a concrete geometric mechanism in Regge gravity, tracing the appearance of massive BMS$_3$ particles to diffeomorphism breaking by conical defects, and highlights the broader relevance of discrete geometry approaches to quantum gravity with matter.