Monte Carlo Simulation of the $SU(2)/\mathbb{Z}_2$ Yang--Mills Theory
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913876101038080 |
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| author | Abe, Motokazu Morikawa, Okuto Suzuki, Hiroshi |
| author_facet | Abe, Motokazu Morikawa, Okuto Suzuki, Hiroshi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00286 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Monte Carlo Simulation of the $SU(2)/\mathbb{Z}_2$ Yang--Mills Theory Abe, Motokazu Morikawa, Okuto Suzuki, Hiroshi High Energy Physics - Lattice High Energy Physics - Theory 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. |
| title | Monte Carlo Simulation of the $SU(2)/\mathbb{Z}_2$ Yang--Mills Theory |
| topic | High Energy Physics - Lattice High Energy Physics - Theory |
| url | https://arxiv.org/abs/2501.00286 |