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

Abstract

We consider recently-constructed solutions of three-dimensional ${SL}(N,{\mathbb{R}})\times {SL}(N,{\mathbb{R}})$ 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 ${SL}(N,{\mathbb{R}})\times {SL}(N,{\mathbb{R}})$ symmetry. We argue that these results pose a challenge to constructing a duality relating these solutions to field theories with non-relativistic symmetries.