Lifshitz Holography with Isotropic Scale Invariance

TL;DR

Problem: can an anisotropic Lifshitz fixed point exhibit isotropic conformal invariance. Approach: build a holographic dual in (2+1)D using a spin-3 higher-spin gravity with a z=2 Lifshitz ground state and impose consistent boundary conditions. Key findings: the asymptotic symmetry algebra is two copies of the W3 algebra with central charge $c=3\ell/(2G_3)$, and the Lifshitz ground state gains AdS-like isometries via higher-spin gauge symmetry, while not being gauge-equivalent to AdS$_3$. Significance: this provides a concrete isotropic conformal structure for Lifshitz fixed points through higher-spin holography and suggests a broader pattern where Lifshitz holography enhances symmetries to $\mathcal{W}$-algebras, with potential implications for dual Lifshitz CFT$_2$s and holographic pathologies.

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 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.