Abstract
We investigate QCD at large by using -symmetric gauge theory, where is the quark-number chemical potential and is temperature. We impose the flavor-dependent twist boundary condition on quarks in QCD. This QCD-like theory has the twist angle as a parameter, and agrees with QCD when and becomes symmetric when . For both QCD and the -symmetric gauge theory, the phase diagram is drawn in – plane with the Polyakov-loop extended Nambu–Jona-Lasinio model. In the -symmetric gauge theory, the Polyakov loop is zero in the confined phase appearing at and . The perfectly confined phase never coexists with the color superconducting (CSC) phase, since finite diquark condensate in the CSC phase breaks symmetry and then makes finite. When , the CSC phase is more stable than the perfectly confined phase at . Meanwhile, the chiral symmetry can be broken in the perfectly confined phase, since the chiral condensate is invariant. Consequently, the perfectly confined phase is divided into the perfectly confined phase without chiral symmetry restoration in a region of and and the perfectly confined phase with chiral symmetry restoration in a region of and . At low temperature, the basic phase structure of -symmetric QCD-like theory remains in QCD. Properties of the sign problem in -symmetric theory are also discussed. We discuss a numerical framework to evaluate observables at from those at .
2 More- Received 13 November 2015
DOI:https://doi.org/10.1103/PhysRevD.93.056009
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