Evidence of a CP broken deconfined phase in 4D SU(2) Yang-Mills theory at $θ=π$ from imaginary $θ$ simulations
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913825918287872 |
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| author | Hirasawa, Mitsuaki Honda, Masazumi Matsumoto, Akira Nishimura, Jun Yosprakob, Atis |
| author_facet | Hirasawa, Mitsuaki Honda, Masazumi Matsumoto, Akira Nishimura, Jun Yosprakob, Atis |
| contents | The spontaneous breaking of CP symmetry in 4D SU($N$) pure Yang-Mills theory at $θ=π$ has recently attracted much attention in the context of the higher-form symmetry and the 't Hooft anomaly matching condition. Here we use Monte Carlo simulations to study the $N=2$ case, which is interesting since it is the case opposite to the large-$N$ limit, where explicit calculations are available. In order to circumvent the severe sign problem due to the $θ$ term for real $θ$, we first obtain results at imaginary $θ$, where the sign problem is absent, and make an analytic continuation to real $θ$. We use the stout smearing in defining the $θ$ term in the action to be used in our simulations. Thus we obtain the expectation value of the topological charge and the deconfining temperature at $θ=π$, and provide an evidence that the CP symmetry, which is spontaneously broken at low temperature, gets restored \emph{strictly above} the deconfining temperature. This conclusion is consistent with the anomaly matching condition and yet differs from the prediction in the large-$N$ limit. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_03683 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Evidence of a CP broken deconfined phase in 4D SU(2) Yang-Mills theory at $θ=π$ from imaginary $θ$ simulations Hirasawa, Mitsuaki Honda, Masazumi Matsumoto, Akira Nishimura, Jun Yosprakob, Atis High Energy Physics - Theory High Energy Physics - Lattice High Energy Physics - Phenomenology The spontaneous breaking of CP symmetry in 4D SU($N$) pure Yang-Mills theory at $θ=π$ has recently attracted much attention in the context of the higher-form symmetry and the 't Hooft anomaly matching condition. Here we use Monte Carlo simulations to study the $N=2$ case, which is interesting since it is the case opposite to the large-$N$ limit, where explicit calculations are available. In order to circumvent the severe sign problem due to the $θ$ term for real $θ$, we first obtain results at imaginary $θ$, where the sign problem is absent, and make an analytic continuation to real $θ$. We use the stout smearing in defining the $θ$ term in the action to be used in our simulations. Thus we obtain the expectation value of the topological charge and the deconfining temperature at $θ=π$, and provide an evidence that the CP symmetry, which is spontaneously broken at low temperature, gets restored \emph{strictly above} the deconfining temperature. This conclusion is consistent with the anomaly matching condition and yet differs from the prediction in the large-$N$ limit. |
| title | Evidence of a CP broken deconfined phase in 4D SU(2) Yang-Mills theory at $θ=π$ from imaginary $θ$ simulations |
| topic | High Energy Physics - Theory High Energy Physics - Lattice High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2412.03683 |