A singular radial connection over B^5 minimizing the Yang-Mills energy

Abstract

We prove that the pullback of the SU(n)-soliton of Chern class $c_2=1$ over ${\mathbb{S}}^4$ via the radial projection $\pi :{\mathbb{B}}^5\setminus \{0\}\to {\mathbb{S}}^4$ minimizes the Yang-Mills energy under the fixed boundary trace constraint. In particular this shows that stationary Yang-Mills connections in high dimension can have singular sets of codimension 5.

14 pages, 2 figures