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

TL;DR

This paper demonstrates that a specific radial connection over the 5-ball minimizes the Yang-Mills energy with a fixed boundary condition, revealing singularities in high-dimensional stationary Yang-Mills connections.

Contribution

It proves the minimality of a radial pullback of an SU(n)-soliton over the 5-ball, highlighting singular sets of codimension 5 in high-dimensional Yang-Mills theory.

Findings

Radial connection minimizes Yang-Mills energy under boundary constraints

Stationary Yang-Mills connections can have codimension 5 singular sets

Explicit construction of energy-minimizing singular connection

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.