Numerical simulation of fractional topological charge in $SU(N)$ gauge theory coupled with $\mathbb{Z}_N$ 2-form gauge fields

TL;DR

This paper numerically demonstrates that coupling $SU(N)$ gauge theory to $Z_N$ 2-form gauge fields results in fractional topological charges, offering insights into topological properties and potential solutions to topological freezing.

Contribution

It provides the first numerical confirmation of fractional topological charge in $SU(N)$ gauge theory coupled with $Z_N$ 2-form gauge fields.

Findings

Topological charge becomes fractional when coupled with $Z_N$ 2-form gauge fields.

Gradient flow smoothing confirms fractional topological charge.

Higher-form fields may address topological freezing issues.

Abstract

The pure $SU(N)$ gauge theory with a $\theta$ term has the $\mathbb{Z}_N$ $1$-form global symmetry. When this symmetry is gauged, it is formally established that the topological charge becomes fractional. In this talk, we generate gauge configurations using the HMC method with coupling to the gauged $\mathbb{Z}_N$ $2$-form gauge field. After smoothing these configurations via the gradient flow method, we numerically confirm that the topological charge has a fractional value. We also anticipate that these higher-form fields can solve the topological freezing problem.