Self-dual and non-self dual axially symmetric caloron solutions in SU(2) Yang-Mills theory

TL;DR

This paper constructs and analyzes new axially symmetric caloron solutions in SU(2) Yang-Mills theory, revealing both self-dual and non-self dual configurations with novel properties and constituent structures.

Contribution

It introduces a numerical construction of new static axially symmetric caloron solutions, including non-self dual types, expanding the understanding of Yang-Mills instanton configurations.

Findings

Existence of new non-self dual caloron solutions

Solutions are labeled by two integers m,n

Solutions include known self-dual periodic instantons

Abstract

New static regular axially symmetric solutions of SU(2) Euclidean Yang-Mills theory are constructed numerically. They represent calorons having trivial Polyakov loop at spacial infinity. The solutions are labeled by two integers $m,n$. It is shown that besides known, charge one self-dual periodic instanton solution, there are other non-self dual solutions of the Yang-Mills equations naturally composed out of pseudoparticle constituents.