Monte Carlo simulation of the $SU(2)/\mathbb{Z}_2$ Yang--Mills theory
| Autor: | Abe, Motokazu, Morikawa, Okuto, Suzuki, Hiroshi |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 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 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. Comment: 23 pages, many figures |
| Databáze: | arXiv |
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