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 selfcontained 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 sixdimensional superconformal field theories via a PenroseWard transform of higher groupoid bundles over a twistor space. This construction reduces the search for nonAbelian selfdual 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 

Pages (fromto)  674–717 
Number of pages  44 
Journal  Fortschritte der Physik 
Volume  64 
Issue number  89 
Early online date  29 Jul 2016 
DOIs  
Publication status  Published  29 Aug 2016 
Keywords
 hepth
 mathph
 math.DG
 math.MP
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Christian Saemann
 School of Mathematical & Computer Sciences  Professor
 School of Mathematical & Computer Sciences, Mathematics  Professor
Person: Academic (Research & Teaching)