Spherically symmetric Dirac-Yang-Mills pairs on Riemannian manifolds

TL;DR

This paper constructs new examples of spherically symmetric coupled Dirac-Yang-Mills pairs on Riemannian 3-manifolds with SU(2) structure, including solutions on product manifolds, marking the first such examples on closed Riemannian spin manifolds.

Contribution

It introduces the first known coupled Dirac-Yang-Mills pairs on closed Riemannian spin manifolds and demonstrates their construction on various product manifolds.

Findings

Constructed spherically symmetric Dirac-Yang-Mills pairs on Riemannian 3-manifolds.

Produced solutions on S^1 x S^2 for specific radii.

Extended the construction to Riemannian products of arbitrary dimension.

Abstract

In this paper we construct examples of spherically symmetric Dirac-Yang-Mills pairs on Riemannian 3-manifolds with the structure group SU(2). This approach yields coupled solutions (i.e. the connection is not a Yang-Mills connection) and among them are solutions on S^1(r_1) x S^2(r_2) for certain radii r_1 and r_2. We further show how to use such pairs to induce Dirac-Yang-Mills pairs on Riemannian products of arbitrary dimension. These are, to the authors' best knowledge, the first examples of coupled Dirac-Yang-Mills pairs on a closed Riemannian spin manifold.