New Conformal Higher Spin Gravities in $3d$

TL;DR

This paper introduces a new class of conformal higher spin gravities in three dimensions, extending previous models with infinitely many finite-field examples, formulated via Chern-Simons actions, and relating to parity anomalies.

Contribution

It proposes a novel class of conformal higher spin gravities in 3D, expanding the theory space with finite-field models and new features like higher-derivative gauge transformations.

Findings

Infinite examples of theories with finite higher spin fields.

Formulation using Chern-Simons actions for extended conformal algebras.

Connection to parity anomaly and partially-massless fields.

Abstract

We propose a new class of conformal higher spin gravities in three dimensions, which extends the one by Pope and Townsend. The main new feature is that there are infinitely many examples of the new theories with a finite number of higher spin fields, much as in the massless case. The action has the Chern-Simons form for a higher spin extension of the conformal algebra. In general, the new theories contain Fradkin-Tseytlin fields with higher derivatives in the gauge transformations, which is reminiscent of partially-massless fields. A relation of the old and new theories to the parity anomaly is pointed out.