RETRACTED: Yang-Mills theory for bundle gerbes

TL;DR

This paper formulates and analyzes Yang-Mills equations for bundle gerbes on Riemannian manifolds, proving existence and classifying instanton solutions in the compact, oriented case, and exploring duality properties.

Contribution

It introduces a Yang-Mills framework for bundle gerbes, proving existence of instantons and describing their moduli space on compact, oriented manifolds.

Findings

Existence of instanton solutions on compact, oriented manifolds.

Complete characterization of the moduli space of instantons.

Discussion of duality in the context of 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.