θ dependence of Tc in SU(2) Yang-Mills theory

A bstract We present an exploratory study to determine the confinement-deconfinement transition temperature at finite θ , T c ( θ ), for the 4d SU(2) pure Yang-Mills theory. Lattice numerical simulations are performed on three spatial sizes N S = 24, 32, 48 with a fixed temporal size N T = 8. We introduce a non-zero θ -angle by the sub-volume method to mitigate the sign problem. By taking advantage of the universality in the second order phase transition and the Binder cumulant of the order parameter, the θ -dependence of T c is determined to be T c ( θ )/ T c (0) = 1 − 0 . 16(2) ( θ / π ) 2 − 0 . 03(4) ( θ / π ) 4 up to θ ∼ 0.9 π . The reliability of the extrapolations in the sub-volume method is extensively checked. We also point out that the temperature dependence of the topological susceptibility should exhibit a singularity with the exponent for the specific heat.