Perturbative construction of self-dual configurations on the torus

TL;DR

This paper introduces a perturbative method to construct non-abelian self-dual SU(2) Yang-Mills configurations on a four-dimensional torus, expanding around known abelian solutions and validating results with lattice gauge theory.

Contribution

It presents a novel perturbative approach to generate self-dual solutions on the torus, extending previous abelian solutions and comparing with numerical lattice results.

Findings

Perturbative expansion successfully constructs non-abelian solutions.

Next-to-leading order results agree with lattice simulations.

Method provides a new analytical tool for studying self-dual configurations.

Abstract

We develop a perturbative expansion which allows the construction of non-abelian self-dual SU(2) Yang-Mills field configurations on the four-dimensional torus with topological charge 1/2. The expansion is performed around the constant field strength abelian solutions found by 't Hooft. Next to leading order calculations are compared with numerical results obtained with lattice gauge theory techniques.