Twistors, Harmonics and Holomorphic Chern-Simons

TL;DR

This paper reformulates N=4 super Yang-Mills theory using a holomorphic Chern-Simons action based on harmonic space's CR structure, connecting it to Penrose transforms and ambitwistor space concepts.

Contribution

It introduces a novel off-shell formulation of N=4 super Yang-Mills via holomorphic Chern-Simons theory on harmonic space with a CR structure.

Findings

Rewrites N=4 SYM as a holomorphic Chern-Simons action.

Establishes a Penrose transform for local operators.

Draws parallels with ambitwistor space constructions.

Abstract

We show that the off-shell N=3 action of N=4 super Yang-Mills can be written as a holomorphic Chern-Simons action whose Dolbeault operator is constructed from a complex-real (CR) structure of harmonic space. We also show that the local space-time operators can be written as a Penrose transform on the coset SU(3)/(U(1) \times U(1)). We observe a strong similarity to ambitwistor space constructions.