Toward semistrict higher gauge theory

Details Toward semistrict higher gauge theory Toward semistrict higher gauge theory

2011-12-13

arxiv.org/abs/1112.2819v2

Physics

High Energy Physics

High Energy Physics - Theory

89 pages, no figures. A few references added. Comments and suggestions are welcome

Scientific paper

We work out a formulation of higher gauge theory, whose symmetry is encoded in a semistrict Lie 2-algebra v and which we call semistrict. We view v as a 2-term L-infinity algebra, a special case of strong homotopy Lie algebra generalizing an ordinary Lie algebra by allowing the Lie bracket to have a non trivial Jacobiator. Fields are v-valued and gauge transformations are special Aut(v)-valued maps organized as an ordinary group and acting on them. The global behaviour of fields is controlled by appropriate gauge transformation 1-cocycles. 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. We discuss merits and weaknesses of our formulation in relations to other approaches.

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