Numerical analysis of fractional charge solutions on the torus

TL;DR

This paper numerically investigates SU(N) Yang-Mills solutions with fractional topological charge on a torus under twisted boundary conditions, analyzing their properties and behavior as N approaches infinity.

Contribution

It introduces a numerical analysis of fractional charge solutions on the torus, highlighting their characteristics and large N behavior.

Findings

Fractional charge solutions have minimal action S=8π²/N.

Properties of solutions vary with N, especially as N approaches infinity.

Numerical methods effectively analyze these non-trivial configurations.

Abstract

We study by numerical methods a particular kind of SU(N) Yang-Mills solutions of the Euclidean equations of motion which appear on the torus when twisted boundary conditions are imposed. These are instanton-like configurations with the peculiarity of having fractional topological charge. We focus on those solutions with minimal non-trivial action $S=8\pi^2/\N$ and extract their properties in a few different cases, paying special attention to the $N \to \infty$ limit.