Higher spin extension of cosmological spacetimes in 3D: asymptotically flat behaviour with chemical potentials and thermodynamics

TL;DR

This paper develops generalized asymptotic conditions for higher spin gravity in three dimensions without cosmological constant, preserving the BMS3 algebra, and explores their thermodynamics and gauge properties, extending to higher spins.

Contribution

It introduces a new set of asymptotic conditions for higher spin gravity in flat 3D spacetimes, connecting them to known AdS conditions and analyzing thermodynamics without explicit gauge group representations.

Findings

Asymptotic conditions preserve BMS3 algebra with higher spin extension.

Thermodynamics derived from gauge fields and topology, not explicit gauge group.

Regularity achieved via gauge fixing and holonomy conditions.

Abstract

A generalized set of asymptotic conditions for higher spin gravity without cosmological constant in three spacetime dimensions is constructed. They include the most general temporal components of the gauge fields that manifestly preserve the original asymptotic higher spin extension of the BMS$_{3}$ algebra, with the same central charge. By virtue of a suitable permissible gauge choice, it is shown that this set can be directly recovered as a limit of the boundary conditions that have been recently constructed in the case of negative cosmological constant, whose asymptotic symmetries are spanned by two copies of the centrally-extended W$_{3}$ algebra. Since the generalized asymptotic conditions allow to incorporate chemical potentials conjugated to the higher spin charges, a higher spin extension of locally flat cosmological spacetimes becomes naturally included within the set. It is shown that their thermodynamic properties can be successfully obtained exclusively in terms of gauge fields and the topology of the Euclidean manifold, which is shown to be the one of a solid torus, but with reversed orientation as compared with one of the black holes. It is also worth highlighting that regularity of the fields can be ensured through a procedure that does not require an explicit matrix representation of the entire gauge group. In few words, we show that the temporal components of generalized dreibeins can be consistently gauged away, which partially fixes the chemical potentials, so that the remaining conditions can just be obtained by requiring the holonomy of the generalized spin connection along a thermal circle to be trivial. The extension of the generalized asymptotically flat behaviour to the case of spins $s\geq2$ is also discussed.