Geometry of minimal energy Yang-Mills connections

TL;DR

This paper investigates the structure of energy-minimizing Yang-Mills connections in four dimensions, revealing that their curvature decomposes into a sum of instantons, thus deepening understanding of their geometric properties.

Contribution

It demonstrates that energy-minimizing connections have curvature decompositions into instantons, providing a converse perspective to known minimization properties.

Findings

Energy-minimizing connections' curvature lies in a subbundle decomposing into instantons.

The study offers a geometric characterization of minimal energy Yang-Mills connections.

Provides insights into the structure of solutions in four-dimensional gauge theory.

Abstract

We study the converse to the statement that instantons are minimizers of the Yang--Mills energy in four dimensions. We show that given an energy minimizing connection, A, the curvature of A takes values in a subbundle of the adjoint bundle which decomposes as a sum of instantons.