Minimal Massive Gravity Coupled to Higher Spins

Abstract

Among three-dimensional massive gravities, Minimal Massive Gravity (MMG) is distinguished by a parameter regime in which the AdS bulk theory and the dual conformal field theory can be simultaneously unitary. We couple MMG to a finite tower of higher-spins by promoting the fields of its first-order formulation to $\mathfrak{sl}(N)$-valued ones. We also present an extended formulation involving a group-valued Stückelberg scalar, which realizes the higher-spin translations broken by the massive deformation. We then construct AdS$_2\times$S$^1$ solutions carrying higher-spin hair specific to the massive theory. Finally, we analyse the mass spectrum of the higher-spin modes around AdS$_3$.