Lifshitz holography with isotropic scale invariance

Abstract

Is it possible for an anisotropic Lifshitz critical point to actually exhibit isotropic conformal invariance? We answer this question in the affirmative by constructing a concrete holographic realization. We study three-dimensional spin-3 higher-spin gauge theory with a z = 2 Lifshitz ground state with non-trivial spin-3 background. We provide consistent boundary conditions and determine the associated asymptotic symmetry algebra. Surprisingly, we find that the algebra consists of two copies of the $$ {\mathcal{W}}_3 $$ extended conformal algebra, which is the extended conformal algebra of an isotropic critical system. Moreover, the central charges are given by 3ℓ/(2G). We consider the possible geometric interpretation of the theory in light of the higher spin gauge invariance and remark on the implications of the asymptotic symmetry analysis.