Nonabelian 2-Forms

TL;DR

This paper explores gauge theories involving nonabelian 2-forms, providing new formulations for connections, field strengths, and gauge transformations, with implications for D-branes and mathematical structures like gerbes.

Contribution

It introduces a novel framework for nonabelian 2-form gauge theories using loop space connections, unifying mathematical and physical perspectives.

Findings

Derived explicit expressions for nonabelian 2-form connections and gauge transformations

Constructed BV sigma model actions including Yang-Mills and BF types

Connected the formalism to mathematical structures like nonabelian gerbes

Abstract

We study gauge theories based on nonabelian 2-forms. Certain connections on loop space give rise to generalized covariant derivatives that include a nonabelian 2-form. This can be used to find rather straightforward expressions for the field strength and gauge transformations. As a special case we recover formulas for connections on nonabelian gerbe, as recently constructed in mathematics. The general construction gives rise to connections on algebra bundles, which might be relevant for D-branes in the presence of torsion. We construct BV sigma model actions for these connections and discuss their gauge fixing. We find both Yang-Mills type and topological BF type actions.