Higher Gauge Theories from Lie n-algebras and Off-Shell Covariantization

TL;DR

This paper develops a supergeometric framework for higher gauge theories using QP-manifolds, revealing special gauge algebra extensions in 5 and 6 dimensions and constructing an off-shell covariantized 5D higher gauge theory.

Contribution

It introduces a supergeometric approach to higher gauge theories with Lie n-algebras and demonstrates off-shell covariantization in 5-dimensional cases.

Findings

Special gauge algebra extensions in 5 and 6 dimensions.

Construction of off-shell covariantized higher gauge theory in 5D.

Relation to existing higher gauge theories like arXiv:1206.5643.

Abstract

We analyze higher gauge theories in various dimensions using a supergeometric method based on a differential graded symplectic manifold, called a QP-manifold, which is closely related to the BRST-BV formalism in gauge theories. Extensions of the Lie 2-algebra gauge structure are formulated within the Lie n-algebra induced by the QP-structure. We find that in 5 and 6 dimensions there are special extensions of the gauge algebra. In these cases, a restriction of the gauge symmetry by imposing constraints on the auxiliary gauge fields leads to a covariantized theory. As an example we show that we can obtain an off-shell covariantized higher gauge theory in 5 dimensions, which is similar to the one proposed in [1] (arxiv:1206.5643).