## 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. We thus arrive at the non-Abelian differential cohomology that describes principal 3-bundles with connective structure.

Original language | English |
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Pages (from-to) | 1147-1188 |

Number of pages | 42 |

Journal | Letters in Mathematical Physics |

Volume | 104 |

Issue number | 9 |

Early online date | 29 May 2014 |

DOIs | |

Publication status | Published - Sep 2014 |

## Keywords

- higher gauge theory
- superconformal field theories
- twistors

## ASJC Scopus subject areas

- Mathematical Physics
- Statistical and Nonlinear Physics