Chiral Higher Spin Gravity in (A)dS${}_4$ and secrets of Chern-Simons Matter Theories

TL;DR

This paper constructs a chiral higher spin gravity theory in (A)dS4 as a deformation of flat space, revealing a special integrable sector of Chern-Simons matter theories that impacts dualities and the understanding of higher spin interactions.

Contribution

It introduces a new formulation of chiral higher spin gravity in (A)dS4 as a Free Differential Algebra, connecting it to integrable sectors of Chern-Simons matter theories.

Findings

Existence of a smooth deformation of flat space higher spin gravity in (A)dS4.

Identification of a closed, likely integrable, sector within Chern-Simons matter theories.

Implications for three-dimensional bosonization duality.

Abstract

Chiral Higher Spin Gravity with cosmological constant is constructed as a Free Differential Algebra, i.e. at the level of equations of motion, which is a smooth deformation of its flat space cousin arXiv:2205.07794. Chiral Higher Spin Gravity is a unique class of local higher spin theories; its very existence implies that there is a closed and, most likely, integrable sub-sector of Chern-Simons Matter Theories, which has important consequences both for the theories themselves and for three-dimensional bosonization duality.