A Twistor Description of Six-Dimensional N=(1,1) Super Yang-Mills Theory

TL;DR

This paper develops a twistor space framework for six-dimensional N=(1,1) super Yang-Mills theory, establishing a correspondence between holomorphic vector bundles and solutions to the field equations, extending four-dimensional twistorial methods.

Contribution

It introduces a novel twistor space for 6D N=(1,1) SYM and demonstrates a one-to-one correspondence with solutions, generalizing 4D twistorial descriptions.

Findings

Established a twistor space for 6D N=(1,1) superspace.

Proved a bijective correspondence between holomorphic bundles and solutions.

Reduced the construction to known 4D super Yang-Mills twistorial descriptions.

Abstract

We present a twistor space that describes super null-lines on six-dimensional N=(1,1) superspace. We then show that there is a one-to-one correspondence between holomorphic vector bundles over this twistor space and solutions to the field equations of N=(1,1) super Yang-Mills theory. Our constructions naturally reduce to those of the twistorial description of maximally supersymmetric Yang-Mills theory in four dimensions.