Numerical studies on the finite-temperature CP restoration in 4D SU(N) gauge theory at θ=π

Recent studies on the't Hooft anomaly matching condition have suggested a nontrivial phase structure in 4D SU(N) gauge theory at θ = π. In the large-N limit, it has been found that CP symmetry at θ = π is 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. The crucial point to note is that the CP restoration can be probed by the sudden change of the tail of the topological charge distribution at θ = 0, which can be seen by simulating the theory at imaginary θ without the sign problem. Our results suggest that the CP restoration at θ = π occurs at temperature higher than the deconfining temperature unlike the situation in the large-N limit. © Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0).