Spherically symmetric Dirac-Yang-Mills pairs on Riemannian manifolds
Differential Geometry
2026-05-07 v2 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.2602.09122,
title = {Spherically symmetric Dirac-Yang-Mills pairs on Riemannian manifolds},
author = {Adam Lindström and Marko Sobak},
journal= {arXiv preprint arXiv:2602.09122},
year = {2026}
}
Comments
Added Theorem 1.2 and the associated Section 6. Comments welcome!