Rotating Higher Spin Partition Functions and Extended BMS Symmetries

TL;DR

The paper develops a comprehensive framework for computing one-loop partition functions of arbitrary spin fields in flat space with angular potentials using the heat-kernel method and the method of images, revealing that these partition functions exponentiate as sums of Poincaré characters. In D=3, it demonstrates a precise match between suitable products of higher-spin partition functions and vacuum characters of extended flat asymptotic symmetry algebras (flat ${ m W}_N$ and super BMS$_3$), supported by a representation-theoretic construction based on coadjoint orbits and induced modules. This establishes a consistent bulk/boundary correspondence for higher-spin theories in flat space, including supersymmetric and hypergravity extensions, and provides a clear path to incorporating more general degrees of freedom such as mixed-symmetry and continuous-spin fields. The work also clarifies regularization subtleties and highlights avenues for connecting flat-space results to AdS holography through controlled flat limits and orbit classifications.

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 Poincaré 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.