Non-Abelian Tensor Multiplet Equations from Twistor Space

TL;DR

This paper develops a twistor space approach to relate holomorphic principal 2-bundles with non-Abelian self-dual tensor fields and supersymmetric extensions in six dimensions, providing a geometric framework for these theories.

Contribution

It introduces a Penrose-Ward transform linking twistor geometry with non-Abelian tensor multiplet equations and their supersymmetric versions in six dimensions.

Findings

Established a bijection between holomorphic 2-bundles and non-Abelian self-dual tensor fields.

Derived supersymmetric constraint equations for N=(1,0) and N=(2,0) theories.

Connected the geometric construction to non-Abelian self-dual strings.

Abstract

We establish a Penrose-Ward transform yielding a bijection between holomorphic principal 2-bundles over a twistor space and non-Abelian self-dual tensor fields on six-dimensional flat space-time. Extending the twistor space to supertwistor space, we derive sets of manifestly N=(1,0) and N=(2,0) supersymmetric non-Abelian constraint equations containing the tensor multiplet. We also demonstrate how this construction leads to constraint equations for non-Abelian supersymmetric self-dual strings.