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

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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.

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  1. Department of Mathematics, Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK

    Christian Sämann

  2. Department of Mathematics, University of Surrey, Guildford, GU2 7XH, UK

    Martin Wolf

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  1. Christian Sämann
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Sämann, C., Wolf, M. Six-Dimensional Superconformal Field Theories from Principal 3-Bundles over Twistor Space. Lett Math Phys 104, 1147–1188 (2014). https://doi.org/10.1007/s11005-014-0704-3

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