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

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.

Comments: 24 pages, many figures. The final version to appear in PTEP