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

Lei, Yang; Ross, Simon F.

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.

Citation

Lei, Y., & Ross, S. F. (2015). Connection versus metric description for non-AdS solutions in higher-spin theories. Classical and Quantum Gravity, 32(18), Article 185005. https://doi.org/10.1088/0264-9381/32/18/185005

• Journal Article Type: Article
• Acceptance Date: Jul 27, 2015
• Publication Date: Sep 24, 2015
• Deposit Date: Sep 21, 2015
• Publicly Available Date: Aug 26, 2016
• Journal: Classical and Quantum Gravity
• Print ISSN: 0264-9381
• Electronic ISSN: 1361-6382
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 32
• Issue: 18
• Article Number: 185005
• DOI: https://doi.org/10.1088/0264-9381/32/18/185005
• Keywords: Lifshitz, Higher-spin, Holography.
• Public URL: https://durham-repository.worktribe.com/output/1431387