Description
I will talk about phases of four dimensional SU(N) pure Yang-Mills theory as changing temperature and theta angle. Recent studies on the 't Hooft anomaly matching condition have suggested a nontrivial phase structure in 4D SU(N) gauge theory at theta =pi. In the large-N limit, it has been found that CP symmetry at theta=pi is spontaneously broken in the confined phase, while it restores in the deconfined phase, which is indeed one of the possible scenarios. However, at small N, one may find other situations that are consistent with the consequence of the anomaly matching condition. Here we investigate this issue for N=2 by direct lattice calculations. We provide numerical support for existence of CP broken deconfined phase at theta=pi in intermediate temperature regime. While my talk is mainly based on my recent joint work with M. Hirasawa, A. Matsumoto, J. Nishimura and A. Yosprakob (arXiv:2412.03683), I will start with introductory materials and discuss possible improvements in future.
