SU(N) fractional Instantons

TL;DR

This paper investigates fractional instanton solutions in SU(N) Yang-Mills theory, focusing on their properties, large N behavior, and implications for tunneling between gauge configurations, using numerical methods with twisted boundary conditions.

Contribution

It introduces a numerical study of fractional topological charge solutions in SU(N) Yang-Mills theory with a novel large N sequence based on Fibonacci numbers.

Findings

Large N scaling of fractional instantons analyzed

Gauge invariant quantities like Polyakov loops studied

Instantons interpreted as tunneling events in Hamiltonian limit

Abstract

We present our study of a set of solutions to the $SU(N)$ Yang-Mills equations of motion with fractional topological charge. The configurations are obtained numerically by minimizing the action with gradient flow techniques on a torus of size $l^2\times(Nl)^2$ with twisted boundary conditions. We pay special attention to the large $N$ limit, which is taken along a very peculiar sequence, with the number of colors $N$ and the magnetic flux $m$ selected respectively as the $n$-th and $n-2$ terms of the Fibonacci sequence. We discuss the large $N$ scaling of the solutions and analyze several gauge invariant quantities as the Polyakov loops. We also discuss the so-called Hamiltonian limit, with one of the large directions sent to infinity, where these instantons represent tunneling events between inequivalent pure gauge configurations.