Instanton-like Contributions to the Dynamics of Yang-Mills Fields on the Twisted Torus

TL;DR

This paper investigates instanton-like solutions in SU(2) lattice gauge theory on a twisted torus, analyzing their impact on energy sector splitting in small-volume settings.

Contribution

It introduces a study of periodic instantons with half-integer topological charge and quantifies their effects on energy flux sector splitting.

Findings

Identification of $Q=1/2$ instantons in small-volume SU(2) lattice gauge theory.

Calculation of their free energy contributions.

Quantification of their role in energy flux sector splitting.

Abstract

We study $SU(2)$ lattice gauge theory in small volumes and with twist $\vec{m}=(1,1,1)$. We investigate the presence of the periodic instantons of $Q=\frac{1}{2}$ and determine their free energy and their contribution to the splitting of energy flux sectors \mbox{$E(\vec{e}=(1,1,1))-E(\vec{e}=(0,0,0)) $.}