2011/12/13 by Roberto Zucchini, Zucchini, Roberto
Mathematics · Physics and Astronomy · #81T13 #81T20 #81T45 #81T70 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #hep-th #math-ph #math.DG #math.MP #msc:81T13 #msc:81T20 #msc:81T45 #msc:81T70
paper · pdf · doi:10.48550/arxiv.1112.2819
158 pages, no figures. Substantially revised and enlarged version of the paper originally titled "Toward semistrict higher gauge theory"
arxiv created 2012/11/10 · arxiv updated 2012/11/13
In the first part of this paper, we work out a perturbative Lagrangian formulation of semistrict higher gauge theory, that avoids the subtleties of the relationship between Lie 2-groups and algebras by relying exclusively on the structure semistrict Lie 2-algebra v and its automorphism 2-group Aut(v). Gauge transformations are defined and shown to form a strict 2-group depending on v. Fields are v-valued and their global behaviour is controlled by appropriate gauge transformation gluing data organized as a strict 2-groupoid. In the second part, using the BV quantization method in the AKSZ geometrical version, we write down a 3-dimensional semistrict higher BF gauge theory generalizing ordinary BF theory, carry out its gauge fixing and obtain as end result a semistrict higher topological gauge field theory of the Witten type. We also introduce a related 4-dimensional semistrict higher Chern-Simons gauge theory.