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arXiv · 2501.00286

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

Motokazu Abe·Okuto Morikawa·Hiroshi Suzuki
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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.

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Motokazu Abe, Okuto Morikawa, Hiroshi Suzuki. 2024-12-31. Monte Carlo Simulation of the $SU(2)/\mathbb{Z}_2$ Yang--Mills Theory. https://arxiv.org/abs/2501.00286

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