Higher-order chiral scalar from boundary reduction of 3d higher-spin gravity

TL;DR

This paper derives a covariant boundary action for higher-spin gravity in 3D, generalizing known scalar actions to arbitrary spin, and explores the structure of zero modes in non-trivial backgrounds.

Contribution

It introduces a covariant boundary reduction procedure for 3D higher-spin gravity, producing higher-order chiral scalars for arbitrary spin and analyzing zero modes in complex backgrounds.

Findings

Derived a Lorentz covariant boundary action for higher-spin scalars.

Generalized scalar actions to arbitrary spin s.

Identified richer zero mode structures in non-trivial backgrounds.

Abstract

We use a recently proposed covariant procedure to reduce the Chern-Simons action of three-dimensional higher-spin gravity to the boundary, resulting in a Lorentz covariant action for higher-order chiral scalars. After gauge-fixing, we obtain a higher-derivative action generalizing the $s=1$ Floreanini-Jackiw and $s=2$ Alekseev-Shatashvili actions to arbitrary spin $s$. For simplicity, we treat the case of general spin at the linearized level, while the full non-linear asymptotic boundary conditions are presented in component form for the $SL(3,\mathbb R)$ case. Finally, we extend the spin-3 linearized analysis to a background with non-trivial higher-spin charge and show that it has a richer structure of zero modes.