AKSZ models of semistrict higher gauge theory

TL;DR

This paper develops a perturbative Lagrangian framework for semistrict higher gauge theories using AKSZ and BV formalisms, introducing new 3D and 4D topological gauge theories based on semistrict Lie 2-algebras.

Contribution

It provides a novel perturbative formulation of semistrict higher gauge theories and constructs new topological gauge theories in 3 and 4 dimensions using AKSZ and BV methods.

Findings

Formulated a gauge theory framework based on semistrict Lie 2-algebras.

Constructed a 3D higher BF gauge theory generalizing ordinary BF theory.

Introduced a 4D semistrict higher Chern-Simons 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.