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

Abstract

The phase diagram on the θ-T plane in four dimensional SU(3) Yang-Mills theory is explored. We revisit the θ dependence of the deconfinement transition temperature, Tc(θ), on the lattice through the constraint effective potential for Polyakov loop. The θ term is introduced by the reweighting method, and the critical β is determined to θ ∼ 0.75, where the interpolation in β is carried out by the multipoint reweighting method. The θ dependence of Tc obtained here turns out to be consistent with the previous result by D’Elia and Negro [1, 2]. We also derive Tc(θ) 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 Tc(θ) becomes higher with θ, which suggests that the first order transition continues robustly above θ ∼ 0.75. Using information obtained here, we try to depict the expected θ dependence of the free energy density at T ≲ Tc(0), which crosses the first order transition line at an intermediate value of θ. 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 $$ \left({\theta}_R,{\theta}_I\right)=\left(\left(2m+1\right)\pi, \frac{2n+1}{2\chi {V}_4}\right) $$ θ R θ I = 2 m + 1 π 2 n + 1 2 χ V 4 with m and n arbitrary integers.