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

Abstract

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=2π/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 μ\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 φ=0, using the heavy quark theory. We discuss a lattice QCD framework to evaluate observables at θ=0 from those at θ=2π/3.

8 pages, 8 figures

References in corpus (18)

• The order of the quantum chromodynamics transition predicted by the standard model of particle physics
• The Phase Structure of the Polyakov--Quark-Meson Model
• Can stochastic quantization evade the sign problem? -- the relativistic Bose gas at finite chemical potential
• Chiral crossover, deconfinement and quarkyonic matter within a Nambu-Jona Lasinio model with the Polyakov loop
• Thermodynamics of the PNJL model
• Critical endpoint in the Polyakov-loop extended NJL model
• Polyakov loop extended NJL model with imaginary chemical potential
• Flux representation of an effective Polyakov loop model for QCD thermodynamics
• Phase diagram in the imaginary chemical potential region and extended Z3 symmetry
• Imaginary Chemical Potential Approach for the Pseudo-Critical Line in the QCD Phase Diagram with Clover-Improved Wilson Fermions
• Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral
• Comparison of complex Langevin and mean field methods applied to effective Polyakov line models
• The QCD phase diagram according to the center group
• Worm algorithms for the 3-state Potts model with magnetic field and chemical potential
• Lattice study on QCD-like theory with exact center symmetry
• The quarkynic phase and the Z_{Nc} symmetry
• Quark number densities at imaginary chemical potential in $N_f=2$ lattice QCD with Wilson fermions and its model analyses
• Positivity of center subsets for QCD

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• Vacuum structure of Yang-Mills theory as a function of $\theta$
• High-temperature domain walls of QCD with imaginary chemical potentials
• Interplay between sign problem and Z_3 symmetry in three-dimensional Potts model
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