Nonabelian Bundle Gerbes, their Differential Geometry and Gauge Theory

TL;DR

This paper explores nonabelian bundle gerbes as higher analogs of principal bundles, detailing their differential geometry and gauge theory aspects, including connections, curving, and curvature, relevant for Yang-Mills theories with 2-form potentials.

Contribution

It introduces a global and local formalism for nonabelian bundle gerbes, extending gauge theory concepts to higher geometric structures.

Findings

Developed a coordinate-independent formalism for nonabelian bundle gerbes

Analyzed gauge transformations and curvature in the higher bundle context

Provided foundational tools for 2-form gauge potential Yang-Mills theories

Abstract

Bundle gerbes are a higher version of line bundles, we present nonabelian bundle gerbes as a higher version of principal bundles. Connection, curving, curvature and gauge transformations are studied both in a global coordinate independent formalism and in local coordinates. These are the gauge fields needed for the construction of Yang-Mills theories with 2-form gauge potential.