Spherically symmetric Dirac-Yang-Mills pairs on Riemannian manifolds

In this paper we construct examples of spherically symmetric Dirac-Yang-Mills pairs on Riemannian 3-manifolds with the structure group 𝐒 𝐔 ⁡ ( 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 ) × 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 certain 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.