We investigate quark–gluon thermodynamics with the symmetry. The flavor-dependent twist boundary condition (TBC) is imposed on Nc degenerate flavor quarks in the SU(Nc) gauge theory. This model is useful to understand the mechanism of color confinement. Thermodynamics of this quark–gluon system is studied by imposing the TBC on the Polyakov-loop extended Nambu–Jona–Lasinio (PNJL) model. The TBC model is applied to two- and three-color cases. The symmetry is preserved below some temperature Tc, but spontaneously broken above Tc. The color confinement below Tc preserves the flavor symmetry. Above Tc, the flavor symmetry is broken, but the breaking is suppressed by the entanglement between the Polyakov loop and the chiral condensate. Particularly at low temperature, dynamics of the TBC model is similar to that of the PNJL model with the standard fermion boundary condition, indicating that the symmetry is a good approximate concept in the latter model even if the current quark mass is small. The present prediction can be tested in future by lattice QCD, since the quark–gluon dynamics with a flavor-dependent imaginary chemical potential has no sign problem.
We investigate differences and similarities between fundamental fermions and adjoint fermions in SU (N ) gauge theories. The gauge theory with fundamental fermions possesses ZN symmetry only in the limit of infinite fermion mass, whereas the gauge theory with adjoint fermions does have the symmetry for any fermion mass. The flavor-dependent twisted boundary condition (FTBC) is then imposed on fundamental fermions so that the theory with fundamental fermions can possess ZN symmetry for any fermion mass. We show similarities between FTBC fundamental fermions and adjoint fermions, using the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model. In the mean-field level, the PNJL model with FTBC fundamental fermions has dynamics similar to the PNJL model with adjoint fermions for the confinement/deconfinement transition related to ZN symmetry. The chiral property is somewhat different between the two models, but there is a simple relation between chiral condensates in the two models. As an interesting high-energy phenomenon, a possibility of the gauge symmetry breaking is studied for FTBC fundamental fermions.
We investigate the confinement mechanism in three-flavor QCD with imaginary isospin chemical po-, using the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model, where T is temperature. As for three degenerate flavors, the system has Z 3 symmetry at θ = 2π/3 and hence the Polyakov loop Φ vanishes there for small T . As for 2+1 flavors, the symmetry is not preserved for any θ, but Φ becomes zero at θ = θ conf < 2π/3 for small T . The confinement phase defined by Φ = 0 is realized, even if the system does not have Z 3 symmetry exactly. In the θ-T plane, there is a critical endpoint of deconfinement transition. The deconfinement crossover at zero chemical potential is a remnant of the first-order deconfinement transition at θ = θ conf . The relation between the non-diagonal element χ us of quark number susceptibilities and the deconfinement transition is studied. The present results can be checked by lattice QCD simulations directly, since the simulations are free from the sign problem for any θ.
We investigate the phase structure of two-color QCD at both real and imaginary chemical potentials (µ), 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 × 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 µ to real µ by comparing lattice QCD results calculated at real µ with the result of analytic function the coefficients of which are determined from lattice QCD results at imaginary µ. 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.
We investigated the phase diagram of SU(3) gauge theory in four dimension with one compact dimension by using the perturbative one-loop effective potential. Effects of the adjoint and fundamental fermions are investigated and then the rich phase structure in the quark-mass and compactsize scale is realized. Our results are qualitatively consistent with the recent lattice calculation and clearly show that the lattice calculation can be understood from the Hosotani mechanism. Moreover, we show the result obtained by using the flavor twisted boundary condition for fundamental fermion which does not break the Z 3 symmetry, explicitly.
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