Actions for Self-dual Higher Spin Gravities

TL;DR

This paper develops covariant actions for self-dual higher spin gravities, extending known theories to include gauge and gravitational interactions in flat and (A)dS spaces, using a novel twistor-inspired approach.

Contribution

It provides the first covariant actions for contractions of Chiral Higher Spin Gravity, simplifying interaction structures and resolving existing puzzles in higher spin theories.

Findings

Constructed covariant actions for higher spin extensions of self-dual theories.

Presented a new twistor-inspired description of higher spin fields.

Achieved a covariant form of minimal gravitational interactions for higher spins.

Abstract

Higher Spin Gravities are scarce, but covariant actions for them are even scarcer. We construct covariant actions for contractions of Chiral Higher Spin Gravity that represent higher spin extensions of self-dual Yang-Mills and self-dual Gravity theories. The actions give examples of complete higher spin theories both in flat and (anti)-de Sitter spaces that feature gauge and gravitational interactions. The actions are based on a new description of higher spin fields, whose origin can be traced to early works on twistor theory. The new description simplifies the structure of interactions. In particular, we find a covariant form of the minimal gravitational interaction for higher spin fields both in flat and anti-de Sitter space, which resolves some of the puzzles in the literature.