$θ$ dependence of $T_c$ in SU(2) Yang-Mills theory
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arXiv
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| Natura: | Preprint |
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2024
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| _version_ | 1866915134035722240 |
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| author | Yamada, Norikazu Yamazaki, Masahito Kitano, Ryuichiro |
| author_facet | Yamada, Norikazu Yamazaki, Masahito Kitano, Ryuichiro |
| contents | We present an exploratory study to determine the confinement-deconfinement transition temperature at finite $θ$, $T_c(θ)$, for the 4d \SU(2) pure Yang-Mills theory. Lattice numerical simulations are performed on three spatial sizes $N_S=24$, $32$, $48$ with a fixed temporal size $N_T=8$. We introduce a non-zero $θ$-angle by the sub-volume method to mitigate the sign problem. By taking advantage of the universality in the second order phase transition and the Binder cumulant of the order parameter, the $θ$-dependence of $T_c$ is determined to be $T_c(θ)/T_c(0)=1-0.16(2)\,(θ/π)^2-0.03(4)\,(θ/π)^4$ up to $θ\sim 0.9\,π$. The reliability of the extrapolations in the sub-volume method is extensively checked. We also point out that the temperature dependence of the topological susceptibility should exhibit a singularity with the exponent for the specific heat. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00375 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $θ$ dependence of $T_c$ in SU(2) Yang-Mills theory Yamada, Norikazu Yamazaki, Masahito Kitano, Ryuichiro High Energy Physics - Lattice High Energy Physics - Theory We present an exploratory study to determine the confinement-deconfinement transition temperature at finite $θ$, $T_c(θ)$, for the 4d \SU(2) pure Yang-Mills theory. Lattice numerical simulations are performed on three spatial sizes $N_S=24$, $32$, $48$ with a fixed temporal size $N_T=8$. We introduce a non-zero $θ$-angle by the sub-volume method to mitigate the sign problem. By taking advantage of the universality in the second order phase transition and the Binder cumulant of the order parameter, the $θ$-dependence of $T_c$ is determined to be $T_c(θ)/T_c(0)=1-0.16(2)\,(θ/π)^2-0.03(4)\,(θ/π)^4$ up to $θ\sim 0.9\,π$. The reliability of the extrapolations in the sub-volume method is extensively checked. We also point out that the temperature dependence of the topological susceptibility should exhibit a singularity with the exponent for the specific heat. |
| title | $θ$ dependence of $T_c$ in SU(2) Yang-Mills theory |
| topic | High Energy Physics - Lattice High Energy Physics - Theory |
| url | https://arxiv.org/abs/2411.00375 |