Monte Carlo Simulation of the <i>SU</i>(2)/ℤ2 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.