Fractional topological charge in $SU(N)$ gauge theories without dynamical quarks

TL;DR

This paper explores the emergence and significance of fractional topological charge configurations in pure $SU(N)$ gauge theories, highlighting their quantum origin, fixed size, and potential detectability via lattice simulations.

Contribution

It provides a detailed analysis and illustrative solutions for fractional topological charges arising as quantum effects in the vacuum of pure gauge theories.

Findings

Fractional topological charges of order 1/N can dominate the vacuum in the confining phase.

These configurations are quantum solutions of the effective Lagrangian, not classical solutions.

Their size is fixed around the confinement scale, and they can be detected through lattice simulations.

Abstract

In $SU(N)$ gauge theories without dynamical quarks, we discuss how configurations with fractional topological charge, $\sim 1/N$, can arise in the vacuum and dominate in the confining phase. They are not solutions of the classical equations of motion, but arise as quantum solutions of the effective Lagrangian. Their size is essentially fixed, on the order of the confinement scale. We give both a general mathematical analysis and illustrative solutions. Their presence can be measured through numerical simulations on the lattice using known methods. As they carry $\mathbb{Z}_N$ magnetic charge, the introduction of dynamical quarks significantly complicates their dynamics.