Connection vs metric description for non-AdS solutions in higher spin theories

TL;DR

This paper investigates non-relativistic solutions in three-dimensional higher-spin theories, revealing that some solutions cannot be fully described by metrics and challenging the duality with non-relativistic field theories.

Contribution

It demonstrates that certain non-relativistic solutions in higher-spin Chern-Simons theories lack metric descriptions and have persistent global symmetries, complicating duality constructions.

Findings

Some solutions are not invertibly mapped to metric solutions.

All solutions exhibit a global SL(N,R) x SL(N,R) symmetry.

These results challenge the duality between higher-spin solutions and non-relativistic field theories.

Abstract

We consider recently-constructed solutions of three dimensional SL(N,R) x SL(N,R) Chern-Simons theories with non-relativistic symmetries. Solutions of the Chern-Simons theories can generically be mapped to solutions of a gravitational theory with a higher-spin gauge symmetry. However, we will show that some of the non-relativistic solutions are not equivalent to metric solutions, as this mapping fails to be invertible. We also show that these Chern-Simons solutions always have a global SL(N,R) x SL(N,R) symmetry. We argue that these results pose a challenge to constructing a duality relating these solutions to field theories with non-relativistic symmetries.