θ dependence of Tc in 4d SU(3) Yang-Mills theory with histogram method and the Lee-Yang zeros in the large N limit

The phase diagram on the theta-T plane in four dimensional SU(3) Yang-Mills theory is explored. We revisit the theta dependence of the deconfinement transition temperature, T-c(theta), on the lattice through the constraint effective potential for Polyakov loop. The theta term is introduced by the reweighting method, and the critical beta is determined to theta similar to 0.75, where the interpolation in beta is carried out by the multipoint reweighting method. The theta dependence of T-c obtained here turns out to be consistent with the previous result by D'Elia and Negro [1, 2]. We also derive T-c(theta) by classifying configurations into the high and low temperature phases and applying the Clausius-Clapeyron equation. It is found that the potential barrier in the double well potential at T-c(theta) becomes higher with theta, which suggests that the first order transition continues robustly above theta similar to 0.75. Using information obtained here, we try to depict the expected theta dependence of the free energy density at T less than or similar to T-c(theta), which crosses the first order transition line at an intermediate value of theta. Finally, how the Lee-Yang zeros associated with the spontaneous CP violation appear is discussed formally in the large N limit, and the locations of them are found to be (theta(R), theta(I)) = ((2m + 1)pi, 2n+1/2 chi V-4 with m, and n arbitrary integers.

Automated summary

The phase diagram on the theta-T plane in four dimensional SU(3) Yang-Mills theory is explored in this study. The dependence of the deconfinement transition temperature, T-c(theta), on theta is investigated using the constraint effective potential for Polyakov loop. It is found that T-c(theta) is consistent with previous results and the potential barrier at T-c(theta) becomes higher with increasing theta, suggesting the presence of a first-order transition above a certain value of theta. Additionally, the expected theta dependence of the free energy density at T less than or similar to T-c(theta) is discussed.