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

TL;DR

The paper derives a non-relativistic, chiral, massive higher-spin gravity in a deformed $AdS_3$ background by applying a Lifshitz deformation and null reduction to chiral HSGRA in $AdS_4$, yielding a 3d NR theory with partially fixed cubic couplings. It develops twist-free torsional Schrödinger geometry as the NR backdrop, derives NR kinematics, bulk-to-boundary propagators, and cubic vertices in this setting, and shows that higher-spin interactions become suppressed at large spin when a mass–spin relation $s \approx \alpha_0 + \alpha' m^{2/\mathtt{z}}$ is invoked. The work argues that the holographic dual is a $2d$ NR Landau–Ginzburg-type theory in the light-cone gauge, describing a two-fluid system constrained along one spatial dimension, suggesting a novel NR holographic correspondence related to critical phenomena and condensed-matter-like dynamics. Overall, it provides a tractable NR reduction of a UV-finite 4d chiral HSGRA and proposes concrete NR observables and dualities, with potential applications to NR criticality and two-fluid physics in low dimensions.

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 $λ$-point constrained in one spatial dimension.