Twisting Twistor space

TL;DR

This work develops a twist-noncommutative gauge-theory framework by embedding Drinfel'd twist deformations into twistor space, preserving the incidence relation and fiber structure to map twistor actions to four-dimensional spacetime theories. The authors construct twisted BF theory and twisted holomorphic Chern-Simons theory on (super)twistor spaces, show their equivalence to noncommutative Yang–Mills and N=4 SYM in four dimensions via fiber integration, and extend the construction to matter fields and the full supersymmetric setting. A key technical ingredient is a differential calculus on twisted spaces that maintains cyclicity under integration, enabling gauge invariance and a consistent Hodge duality, with careful treatment of SD/ASD sectors through a star-product basis. The results provide a robust twist-based route to noncommutative gauge theories in a twistor context, offering a natural platform for studying twisted amplitude techniques and potential links to integrable structures within noncommutative settings.

Abstract

We construct twisted noncommutative gauge theories on twistor space and show that they are equivalent to four-dimensional twist-noncommutative gauge theories. In particular, we study twists of the Poincaré algebra. We explain how such a twist leads to twisted noncommutative twistor space and how to construct noncommutative versions of BF theory and holomorphic Chern-Simons theory on noncommutative supertwistor space. We show how those theories are equivalent to noncommutative versions of Yang-Mills theory and supersymmetric Yang-Mills theory, respectively.