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Higher Groupoid Bundles, Higher Spaces, and Self-Dual Tensor Field Equations

Wolf, M, Jurco, B and Saemann, C (2016) Higher Groupoid Bundles, Higher Spaces, and Self-Dual Tensor Field Equations Fortschritte der Physik / Progress of Physics, 64 (8-9). pp. 674-717.

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Abstract

We develop a description of higher gauge theory with higher groupoids as gauge structure from first principles. This approach captures ordinary gauge theories and gauged sigma models as well as their categorifications on a very general class of (higher) spaces comprising presentable differentiable stacks, as e.g. orbifolds. We start off with a self-contained review on simplicial sets as models of (∞,1)-categories. We then discuss principal bundles in terms of simplicial maps and their homotopies. We explain in detail a differentiation procedure, suggested by Severa, that maps higher groupoids to L∞-algebroids. Generalising this procedure, we define connections for higher groupoid bundles. As an application, we obtain six-dimensional superconformal field theories via a Penrose-Ward transform of higher groupoid bundles over a twistor space. This construction reduces the search for non-Abelian self-dual tensor field equations in six dimensions to a search for the appropriate (higher) gauge structure. The treatment aims to be accessible to theoretical physicists.

Item Type: Article
Subjects : subj_Mathematics
Authors :
AuthorsEmailORCID
Wolf, MUNSPECIFIEDUNSPECIFIED
Jurco, BUNSPECIFIEDUNSPECIFIED
Saemann, CUNSPECIFIEDUNSPECIFIED
Date : 29 July 2016
Identification Number : 10.1002/prop.201600031
Copyright Disclaimer : This is an arXiv version of the paper.
Related URLs :
Depositing User : Symplectic Elements
Date Deposited : 25 May 2016 09:49
Last Modified : 27 Oct 2016 11:18
URI: http://epubs.surrey.ac.uk/id/eprint/810814

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