Conformal Higher Spin Theory and Twistor Space Actions

TL;DR

This paper develops a twistor space formulation for conformal higher spin theories, including self-dual and full theories, providing new geometric insights and consistent interaction structures for infinite higher-spin fields.

Contribution

It introduces twistor space actions for conformal higher spin theories, including self-dual and full interactions, with a novel geometric interpretation and a ghost-free subsector.

Findings

Constructed twistor space actions for self-dual higher spin theories.

Identified a ghost-free subsector analogous to Einstein gravity embedding.

Provided a geometric interpretation of higher-spin equations as integrability conditions.

Abstract

We consider the twistor description of conformal higher spin theories and give twistor space actions for the self-dual sector of theories with spin greater than two that produce the correct flat space-time spectrum. We identify a ghost-free subsector, analogous to the embedding of Einstein gravity with cosmological constant in Weyl gravity, which generates the unique spin-s three-point anti-MHV amplitude consistent with Poincare invariance and helicity constraints. By including interactions between the infinite tower of higher-spin fields we give a geometric interpretation to the twistor equations of motion as the integrability condition for a holomorphic structure on an infinite jet bundle. Finally, we introduce anti-self-dual interaction terms to define a twistor action for the full conformal higher spin theory.