Twistor Constructions for Higher-spin Extensions of (Self-dual) Yang-Mills

TL;DR

This paper develops twistor space methods for higher-spin extensions of self-dual Yang-Mills theory, introducing a new twistor action for a higher-spin Yang-Mills generalization.

Contribution

It provides the inverse Penrose transform for higher-spin SDYM and introduces a new twistor action for higher-spin Yang-Mills theory, extending existing frameworks.

Findings

Derived the inverse Penrose transform for higher-spin SDYM.

Formulated a twistor action for higher-spin Yang-Mills theory.

Identified a deformation from self-dual to full higher-spin Yang-Mills.

Abstract

We present the inverse Penrose transform (the map from spacetime to twistor space) for self-dual Yang-Mills (SDYM) and its higher-spin extensions on a flat background. The twistor action for the higher-spin extension of SDYM (HS-SDYM) is of BF-type. By considering a deformation away from the self-dual sector of HS-SDYM, we discover a new action that describes a higher-spin extension of Yang-Mills theory (HS-YM). The twistor action for HS-YM is a straightforward generalization of the Yang-Mills one.