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arXiv · 2502.09115

Numerical evidence for a CP broken deconfined phase at $\theta =\pi$ in 4D SU(2) Yang-Mills theory through simulations at imaginary $\theta$

Mitsuaki Hirasawa·Masazumi Honda·Akira Matsumoto·Jun Nishimura·Atis Yosprakob
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Abstract

We investigate the possibility of the spontaneous breaking of CP symmetry in 4D SU(2) Yang-Mills at $\theta=\pi$, which has recently attracted much attention in the context of the higher-form symmetry and the 't Hooft anomaly matching condition. Here we provide a numerical evidence that the CP symmetry is indeed spontaneously broken at low temperature and it gets restored above the deconfining temperature at $\theta=\pi$, which is consistent with the anomaly matching condition and yet differs from the situation predicted in the large-$N$ limit. We avoid the severe sign problem by performing simulations at imaginary $\theta$. We obtain the critical temperature of the CP restoration and that of deconfinement at $\theta=\pi$ by analytic continuation, which leads to the above conclusion.

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Mitsuaki Hirasawa, Masazumi Honda, Akira Matsumoto, Jun Nishimura, Atis Yosprakob. 2025-02-13. Numerical evidence for a CP broken deconfined phase at $\theta =\pi$ in 4D SU(2) Yang-Mills theory through simulations at imaginary $\theta$. https://arxiv.org/abs/2502.09115

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