Asymptotically flat spacetimes in three-dimensional higher spin gravity

TL;DR

The paper constructs precise asymptotic conditions for three-dimensional higher-spin gravity with vanishing cosmological constant and shows the corresponding asymptotic symmetry algebra is a higher-spin extension of the BMS$_3$ algebra with a nontrivial central extension. This flat-space structure is shown to emerge from a suitable gauge choice that connects to the asymptotically AdS$_3$ boundary data in the $\Lambda\to 0$ limit, and the analysis extends to spins $s\ge 2$. The work provides a Chern-Simons formulation, elucidates the role of higher-spin fields in the charge algebra (including nonlinearities via $W_n$, $V_n$), and demonstrates that the metric and higher-spin fields decouple at the level of backreaction in the chosen gauge while still forming a nontrivial symmetry structure. These results pave the way for a flat-space holographic perspective for higher spins and suggest connections to flat Toda-like theories, with several avenues for further exploration of the solution space and holonomy properties.

Abstract

A consistent set of asymptotic conditions for higher spin gravity in three dimensions is proposed in the case of vanishing cosmological constant. The asymptotic symmetries are found to be spanned by a higher spin extension of the BMS3 algebra with an appropriate central extension. It is also shown that our results can be recovered from the ones recently found for asymptotically AdS3 spacetimes by virtue of a suitable gauge choice that allows to perform the vanishing cosmological constant limit.