Toward Semistrict Higher Gauge Theory
Year: 2011
Type: preprint
Abstract: 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∞ 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. MSC classes: 81T13, 81T20, 81T45, 81T70.
Source: arXiv (Cornell University)
Author: Roberto Zucchini
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2536832189