BMS Particles in Three Dimensions

TL;DR

This thesis explores the group-theoretic structure of three-dimensional quantum gravity, focusing on BMS particles, their representations, thermodynamics, and extensions to higher-spin theories and supergravity.

Contribution

It establishes the connection between BMS group representations and gravitational perturbations, introducing BMS particles and analyzing their thermodynamics within a unified framework.

Findings

BMS particles correspond to unitary representations of asymptotic symmetry groups.

BMS characters match gravitational one-loop partition functions.

Extension of analysis to higher-spin theories and supergravity.

Abstract

This thesis is devoted to the group-theoretic aspects of three-dimensional quantum gravity on Anti-de Sitter and Minkowskian backgrounds. In particular we describe the relation between unitary representations of asymptotic symmetry groups and gravitational perturbations around a space-time metric. In the asymptotically flat case this leads to "BMS particles", representing standard relativistic particles dressed with gravitational degrees of freedom accounted for by coadjoint orbits of the Virasoro group. Their thermodynamics are described by BMS characters, which coincide with gravitational one-loop partition functions. We also extend these considerations to higher-spin theories and supergravity.