Six-Dimensional Superconformal Field Theories from Principal 3-Bundles over Twistor Space

TL;DR

This paper develops six-dimensional superconformal field theories with non-Abelian tensor multiplets using principal 3-bundles over twistor space, extending higher gauge theories and revealing new structures through a Penrose-Ward transform.

Contribution

It introduces a novel construction of superconformal theories from principal 3-bundles, generalizing previous models and systematically relaxing the Peiffer identity.

Findings

Principal 3-bundles encode solutions to self-dual tensor theories.

The Penrose-Ward transform reveals new higher gauge structures.

Formulation of non-Abelian differential cohomology for principal 3-bundles.

Abstract

We construct manifestly superconformal field theories in six dimensions which contain a non-Abelian tensor multiplet. In particular, we show how principal 3-bundles over a suitable twistor space encode solutions to these self-dual tensor field theories via a Penrose-Ward transform. The resulting higher or categorified gauge theories significantly generalise those obtained previously from principal 2-bundles in that the so-called Peiffer identity is relaxed in a systematic fashion. This transform also exposes various unexplored structures of higher gauge theories modelled on principal 3-bundles such as the relevant gauge transformations. This enables us to formulate the non-Abelian differential cohomology that describes principal 3-bundles with connective structures.