Understanding of QCD at high density from Z3-symmetric QCD-like theory
Abstract
We investigate QCD at large mu/T by using Z3-symmetric SU(3) gauge theory, where mu is the quark-number chemical potential and T is temperature. We impose the flavor-dependent twist boundary condition on quarks in QCD. This QCD-like theory has the twist angle theta as a parameter, and agrees with QCD when theta=0 and becomes symmetric when theta=2π/3. For both QCD and the Z3-symmetric SU(3) gauge theory, the phase diagram is drawn in mu--T plane with the Polyakov-loop extended Nambu--Jona-Lasinio model. In the Z3-symmetric SU(3) gauge theory, the Polyakov loop varphi is zero in the confined phase appearing at T 200 MeV. The perfectly confined phase never coexists with the color superconducting (CSC) phase, since finite diquark condensate in the CSC phase breaks Z3 symmetry and then makes varphi finite. When mu 300 MeV, the CSC phase is more stable than the perfectly confined phase at T 100 MeV. Meanwhile, the chiral symmetry can be broken in the perfectly confined phase, since the chiral condensate is Z3 invariant. Consequently, the perfectly confined phase is divided into the perfectly confined phase without chiral symmetry restoration in a region of mu 300 MeV and T 200 MeV and the perfectly confined phase with chiral symmetry restoration in a region of μ 300 MeV and 100 T 200 MeV. The basic phase structure of Z3-symmetric QCD-like theory remains in QCD. We show that in the perfectly confined phase the sign problem becomes less serious because of =0, using the heavy quark theory. We discuss a lattice QCD framework to evaluate observables at θ=0 from those at θ=2π/3.