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

Branislav Jurco, Christian Saemann, Martin Wolf

Research output: Contribution to journalArticle

13 Citations (Scopus)

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 $(\infty,1)$-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 $L_\infty$-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.
Original language English 674–717 44 Fortschritte der Physik 64 8-9 29 Jul 2016 https://doi.org/10.1002/prop.201600031 Published - 29 Aug 2016

• hep-th
• math-ph
• math.DG
• math.MP