Letters in Mathematical Physics

, Volume 104, Issue 9, pp 1147–1188 | Cite as

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

Article

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.

Mathematics Subject Classification (2010)

18F99 53C28 14D21 

Keywords

twistors superconformal field theories higher gauge theory 

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© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Mathematics, Maxwell Institute for Mathematical SciencesHeriot-Watt UniversityEdinburghUK
  2. 2.Department of MathematicsUniversity of SurreyGuildfordUK

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