Monte Carlo Simulation of the $SU(2)/\mathbb{Z}_2$ Yang--Mills Theory

TL;DR

This paper presents a hybrid Monte Carlo simulation of the $SU(2)/ ext{ extonehalfwidth}Z_2$ Yang--Mills theory, demonstrating reduced autocorrelation times and potential advantages for simulating $SU(N)$ gauge theories with dynamical fermions.

Contribution

The authors develop a hybrid Monte Carlo algorithm explicitly incorporating the $ ext{ extonehalfwidth}Z_N$ 2-form gauge field, improving simulation efficiency for $SU(N)/ ext{ extonehalfwidth}Z_N$ theories.

Findings

Significant reduction in autocorrelation lengths for topological charge.

Potential for efficient large-volume simulations of $SU(N)$ theories.

Discussion of incorporating fundamental fermions with fractional baryon number.

Abstract

We carry out a hybrid Monte Carlo (HMC) simulation of the $SU(2)/\mathbb{Z}_2$ Yang--Mills theory in which the $\mathbb{Z}_N$ 2-form flat gauge field (the 't~Hooft flux) is explicitly treated as one of the dynamical variables. We observe that our HMC algorithm in the $SU(2)/\mathbb{Z}_2$ theory drastically reduces autocorrelation lengths of the topological charge and of a physical quantity which couples to slow modes in the conventional HMC simulation of the $SU(2)$ theory. Provided that sufficiently large lattice volumes are available, therefore, the HMC algorithm of the $SU(N)/\mathbb{Z}_N$ theory could be employed as an alternative for the simulation of the $SU(N)$ Yang--Mills theory, because local observables are expected to be insensitive to the difference between $SU(N)$ and~$SU(N)/\mathbb{Z}_N$ in the large volume limit. A possible method to incorporate quarks [fermions in the fundamental representation of~$SU(N)$ with the baryon number~$1/N$] in this framework is also considered.