Evidence of a CP broken deconfined phase in 4D SU(2) Yang-Mills theory at $\theta =\pi$ from imaginary $\theta$ simulations

The spontaneous breaking of CP symmetry in 4D SU($N$) pure Yang-Mills theory at $\theta=\pi$ 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 intere...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Hirasawa, Mitsuaki, Honda, Masazumi, Matsumoto, Akira, Nishimura, Jun, Yosprakob, Atis
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext bestellen
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:The spontaneous breaking of CP symmetry in 4D SU($N$) pure Yang-Mills theory at $\theta=\pi$ 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 $\theta$ term for real $\theta$, we first obtain results at imaginary $\theta$, where the sign problem is absent, and make an analytic continuation to real $\theta$. We use the stout smearing in defining the $\theta$ 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 $\theta=\pi$, 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.
DOI:10.48550/arxiv.2412.03683