Speaker
Description
Recent studies on the 't Hooft anomaly matching condition for 4D SU($N$) gauge theory have suggested that the phase structure at $\theta=\pi$ should be nontrivial. Namely, some symmetry will be spontaneously broken, or gapless modes will appear. In the large-$N$ limit, it is known that CP symmetry at $\theta=\pi$ is broken in the confined phase, while it restores in the deconfined phase, which is indeed one of the consequence of the anomaly matching. However, at small $N$, one may find a qualitatively different phase structure, which will be another possible scenario consistent with the anomaly matching. Here we investigate this issue for $N=2$ by direct lattice calculations. The crucial point of our method is that the restoration of CP symmetry can be probed by the sudden change of the topological charge distribution at $\theta=0$, which can be seen by simulating the theory at imaginary $\theta$ without the sign problem. Our results suggest that the CP symmetry at $\theta=\pi$ is restored at higher temperature than the deconfining temperature unlike the situation in the large-$N$ limit.
