Lifshitz Holography with Isotropic Scale Invariance

TL;DR

This paper demonstrates that a Lifshitz critical point with anisotropic scaling can exhibit isotropic conformal invariance through a holographic model involving three-dimensional higher-spin gauge theory, revealing unexpected symmetry structures.

Contribution

The authors construct a holographic realization showing isotropic conformal invariance emerging from an anisotropic Lifshitz ground state in higher-spin gauge theory.

Findings

Asymptotic symmetry algebra includes two copies of W_3 extended conformal algebra.

Central charges are calculated as 3l/(2G).

The geometric interpretation aligns with higher spin gauge 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 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.