Rotating Higher Spin Partition Functions and Extended BMS Symmetries

TL;DR

This paper computes higher-spin partition functions in flat space, relates them to asymptotic symmetry algebras, and explores their representations, extending results to supergravity and fermionic fields.

Contribution

It provides a novel link between higher-spin partition functions and extended BMS symmetries, including the construction of their unitary representations.

Findings

Partition functions expressed as Poincaré characters.

Matching of partition functions with vacuum characters of extended BMS algebras.

Extension of analysis to supergravity and higher-spin fermionic theories.

Abstract

We evaluate one-loop partition functions of higher-spin fields in thermal flat space with angular potentials; this computation is performed in arbitrary space-time dimension, and the result is a simple combination of Poincar\'e characters. We then focus on dimension three, showing that suitable products of one-loop partition functions coincide with vacuum characters of higher-spin asymptotic symmetry algebras at null infinity. These are extensions of the bms_3 algebra that emerges in pure gravity, and we propose a way to build their unitary representations and to compute the associated characters. We also extend our investigations to supergravity and to a class of gauge theories involving higher-spin fermionic fields.