Three-dimensional non-relativistic chiral massive higher-spin gravity

TL;DR

This paper constructs a non-relativistic chiral massive higher-spin gravity in a deformed $AdS_3$ spacetime, proposing a mass-spin relation and conjecturing a dual 2D non-relativistic Landau-Ginzburg theory.

Contribution

It introduces a novel non-relativistic higher-spin gravity model via Lifshitz deformation and null reduction, with an approximate mass-spin relation and a conjectured holographic dual.

Findings

Higher-spin interactions are suppressed at large spins.

Vertices are less constrained than in the original 4D theory.

The proposed dual is a 2D non-relativistic Landau-Ginzburg theory.

Abstract

We obtain a non-relativistic chiral massive higher-spin gravity in a deformed $AdS_3$ spacetime by applying a Lifshitz deformation and subsequent null reduction to chiral massless higher-spin gravity in $AdS_4$. Intriguingly, the vertices of this non-relativistic theory are less constrained than the ones of the original $4d$ chiral massless theory since we do not have enough dynamical generators to fix the couplings uniquely. Anticipating higher-spin interactions should be suppressed, we propose a simple approximate mass-spin relation which interpolates between the relativistic and non-relativistic regimes. With the proposed mass-spin relation, we observe that that higher-spin interactions indeed become suppressed at large spins, consistent with low-energy physics. We conjecture that the holographic dual of the non-relativistic chiral massive higher-spin gravity proposed in this work is a $2d$ non-relativistic Landau-Ginzburg theory in the light-cone gauge. This non-relativistic theory is expected to describe a two-fluid system with a $\lambda$-point constrained in one spatial dimension.