Determination of the CP restoration temperature at $θ=π$ in 4D SU(2) Yang-Mills theory through simulations at imaginary $θ$
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911754837032960 |
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| author | Hirasawa, Mitsuaki Hatakeyama, Kohta Honda, Masazumi Matsumoto, Akira Nishimura, Jun Yosprakob, Atis |
| author_facet | Hirasawa, Mitsuaki Hatakeyama, Kohta Honda, Masazumi Matsumoto, Akira Nishimura, Jun Yosprakob, Atis |
| contents | The 't Hooft anomaly matching condition provides constraints on the phase structure at $θ=π$ in 4D SU($N$) Yang-Mills theory. In particular, assuming that the theory is confined and the CP symmetry is spontaneously broken at low temperature, it cannot be restored below the deconfining temperature at $θ=π$. Here we investigate the CP restoration at $θ=π$ in the 4D SU(2) case and provide numerical evidence that the CP restoration occurs at a temperature higher than the deconfining temperature unlike the known results in the large-$N$ limit, where the CP restoration occurs precisely at the deconfining temperature. The severe sign problem at $θ=π$ is avoided by focusing on the tail of the topological charge distribution at $θ=0$, which can be probed by performing simulations at imaginary $θ$. By analytic continuation with respect to $θ$, we obtain the topological charge at real $θ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05726 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Determination of the CP restoration temperature at $θ=π$ in 4D SU(2) Yang-Mills theory through simulations at imaginary $θ$ Hirasawa, Mitsuaki Hatakeyama, Kohta Honda, Masazumi Matsumoto, Akira Nishimura, Jun Yosprakob, Atis High Energy Physics - Lattice High Energy Physics - Theory The 't Hooft anomaly matching condition provides constraints on the phase structure at $θ=π$ in 4D SU($N$) Yang-Mills theory. In particular, assuming that the theory is confined and the CP symmetry is spontaneously broken at low temperature, it cannot be restored below the deconfining temperature at $θ=π$. Here we investigate the CP restoration at $θ=π$ in the 4D SU(2) case and provide numerical evidence that the CP restoration occurs at a temperature higher than the deconfining temperature unlike the known results in the large-$N$ limit, where the CP restoration occurs precisely at the deconfining temperature. The severe sign problem at $θ=π$ is avoided by focusing on the tail of the topological charge distribution at $θ=0$, which can be probed by performing simulations at imaginary $θ$. By analytic continuation with respect to $θ$, we obtain the topological charge at real $θ$. |
| title | Determination of the CP restoration temperature at $θ=π$ in 4D SU(2) Yang-Mills theory through simulations at imaginary $θ$ |
| topic | High Energy Physics - Lattice High Energy Physics - Theory |
| url | https://arxiv.org/abs/2401.05726 |