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Three-dimensional nonrelativistic chiral massive higher-spin gravity

Arpita Mitra1,*, Debangshu Mukherjee2,†, and Tung Tran3,‡

  • *Contact author: arpita.mit@mahidol.ac.th
  • †Contact author: debangshum@postech.ac.kr
  • ‡Contact author: tung.tran@khu.ac.kr
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Phys. Rev. D 113, 106012 – Published 12 May, 2026

DOI: https://doi.org/10.1103/xdsn-r46f

Abstract

We obtain a nonrelativistic chiral massive higher-spin gravity in a deformed AdS3 spacetime by applying a Lifshitz deformation and subsequent null reduction to chiral massless higher-spin gravity in AdS4. Intriguingly, the vertices of this nonrelativistic theory are less constrained than the ones in 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 that interpolates between the relativistic and nonrelativistic regimes. With the proposed mass-spin relation, we observe that higher-spin interactions indeed become suppressed at large spins, consistent with low-energy physics. We conjecture that the holographic dual of the nonrelativistic chiral massive higher-spin gravity proposed in this work is a 2d nonrelativistic Landau-Ginzburg theory in the light-cone gauge. This nonrelativistic theory is expected to describe a two-fluid system with a λ-point constrained in one spatial dimension.

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Phys. Rev. D 113, 106012– Published 12 May, 2026
  • Received 18 December 2025
  • Accepted 2 March 2026
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