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