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

Yang Lei, Simon F Ross
2015 Classical and quantum gravity  
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)
more » ... e 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.
doi:10.1088/0264-9381/32/18/185005 fatcat:5yq5ezkgirdmhkdpvsbj4ew2em