Understanding of QCD at high density from Z3-symmetric QCD-like theory

We investigate QCD at large mu/T by using Z_3-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=2pi/3. For both QCD and the Z_3-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 Z_3-symmetric SU(3) gauge theory, the Polyakov loop varphi is zero in the confined phase appearing at T lsim 200 MeV. The perfectly confined phase never coexists with the color superconducting (CSC) phase, since finite diquark condensate in the CSC phase breaks Z_3 symmetry and then makes varphi finite. When mu gsim 300 MeV, the CSC phase is more stable than the perfectly confined phase at T lsim 100 MeV. Meanwhile, the chiral symmetry can be broken in the perfectly confined phase, since the chiral condensate is Z_3 invariant. Consequently, the perfectly confined phase is divided into the perfectly confined phase without chiral symmetry restoration in a region of mu lsim 300 MeV and T lsim 200 MeV and the perfectly confined phase with chiral symmetry restoration in a region of mu gsim 300 MeV and 100 lsim T lsim 200 MeV. The basic phase structure of Z_3-symmetric QCD-like theory remains in QCD. We show that in the perfectly confined phase the sign problem becomes less serious because of varphi=0, using the heavy quark theory. We discuss a lattice QCD framework to evaluate observables at theta=0 from those at theta=2pi/3.

Phase structure of two-color QCD at real and imaginary chemical potentials; lattice simulations and model analyses

We investigate the phase structure of two-color QCD at both real and imaginary chemical potentials mu, performing lattice simulations and analyzing the data with the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. Lattice QCD simulations are done on an 8^3 times 4 lattice with the clover-improved two-flavor Wilson fermion action and the renormalization-group improved Iwasaki gauge action. We test the analytic continuation of physical quantities from imaginary mu to real mu by comparing lattice QCD results calculated at real mu with the result of analytic function the coefficients of which are determined from lattice QCD results at imaginary mu. We also test the validity of the PNJL model by comparing model results with lattice QCD ones. The PNJL model is good in the deconfinement region, but less accurate in the transition and confinement regions. This problem is improved by introducing the baryon degree of freedom to the model. It is also found that the vector-type four-quark interaction is necessary to explain lattice data on the quark number density.