AKSZ models of semistrict higher gauge theory
Abstract
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.
Keywords
Cite
@article{arxiv.1112.2819,
title = {AKSZ models of semistrict higher gauge theory},
author = {Roberto Zucchini},
journal= {arXiv preprint arXiv:1112.2819},
year = {2012}
}
Comments
158 pages, no figures. Substantially revised and enlarged version of the paper originally titled "Toward semistrict higher gauge theory"