Determination of the CP restoration temperature at θ=π in 4D SU(2) Yang-Mills theory through simulations at imaginary θ

The 't Hooft anomaly matching condition provides constraints on the phase structure at θ=π in 4D SU(N ) Yang-Mills theory. In particular, assuming that the theory is confined and the CP symmetry is spontaneously broken at low temperature, it cannot be restored below the deconfining temperature at θ=π . Here we investigate the CP restoration at θ=π in the 4D SU(2) case and provide numerical evidence that the CP restoration occurs at a temperature higher than the deconfining temperature unlike the known results in the large-N limit, where the CP restoration occurs precisely at the deconfining temperature. The severe sign problem at θ=π is avoided by focusing on the tail of the topological charge distribution at θ=0 , which can be probed by performing simulations at imaginary θ . By analytic continuation with respect to θ , we obtain the topological charge at real θ .