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.

21 pages, no figures; v2: references & minor comments added

References in corpus (9)

• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• Holography for Schrodinger backgrounds
• Pathologies in Asymptotically Lifshitz Spacetimes
• Lifshitz Holography with Isotropic Scale Invariance
• Metric- and frame-like higher-spin gauge theories in three dimensions
• Higher Spin Lifshitz Theory and Integrable Systems

Cited by in corpus (6)

• Non-Relativistic Chern-Simons Theories and Three-Dimensional Horava-Lifshitz Gravity
• Three-dimensional Spin-3 Theories Based on General Kinematical Algebras
• The non-linear coupled spin 2 - spin 3 Cotton equation in three dimensions
• Null warped AdS in higher spin gravity
• Higher spin holography with Galilean symmetry in general dimensions
• Notes on su$(1,2)\oplus$u$(1)$ Chern-Simons theory and Torsional Newton-Cartan gravity