Yang-Mills theory for bundle gerbes

Abstract

Given a bundle gerbe with connection on an oriented Riemannian manifold of dimension at least equal to 3, we formulate and study the associated Yang–Mills equations. When the Riemannian manifold is compact and oriented, we prove the existence of instanton solutions to the equations and also determine the moduli space of instantons, thus giving a complete analysis in this case. We also discuss duality in this context.