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 \( \left({\theta}_R,{\theta}_I\right)=\left(\left(2m+1\right)\pi, \frac{2n+1}{2\chi {V}_4}\right) \) with m and n arbitrary integers.
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Otake, N., Yamada, N. θ dependence of Tc in 4d SU(3) Yang-Mills theory with histogram method and the Lee-Yang zeros in the large N limit. J. High Energ. Phys. 2022, 44 (2022). https://doi.org/10.1007/JHEP06(2022)044
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DOI: https://doi.org/10.1007/JHEP06(2022)044