Takahiro Makiyama

Confinement and

We investigate the relation between the confinement and the Z3 symmetry in three-flavor QCD with imaginary isospin chemical potentials (μu ,μ d ,μ s) = (iθ T, −iθ T,0), using the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model, where T is temperature. As for three-degenerate flavors, the system has Z3 symmetry at θ = 2 π/ 3 and hence the Polyakov loopvanishes there for small T. As for 2+1 flavors, the symmetry is not preserved for any θ, butbecomes zero at θ = θconf < 2 π/ 3 for small T. The confinement phase defined by � = 0 is realized, even if the system does not have Z3 symmetry exactly.Inthe θ-T plane,thereisacriticalendpointofdeconfinementtransition. The deconfinement crossover at zero chemical potential is a remnant of the first-order deconfinement transition at θ = θconf. The relation between the non- diagonal element χus 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. (Some figures may appear in colour only in the online journal)

\mathbb {Z}_{3}

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.

symmetry in three-flavor QCD

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.

Differences and similarities between fundamental and adjoint matters in SU(N) gauge theories

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.

Quark?gluon thermodynamics with the

We propose a simple model with the 3 symmetry in order to answer whether the symmetry is a good concept in QCD with light quark mass. The model is constructed by imposing the flavor-dependent twisted boundary condition (TBC) on the three-flavor Polyakov-loop extended Nambu-Jona-Lasinio model. In the model, the 3 symmetry is preserved below some temperature Tc, but spontaneously broken above Tc. Dynamics of the simple model is similar to that of the original PNJL model without the TBC, indicating that the 3 symmetry is a good concept. We also investigate the interplay between the 3 symmetry and the emergence of the quarkyonic phase.

{Z}_{N_c}

We propose a simple model with the 3 symmetry in order to answer whether the symmetry is a good concept in QCD with light quark mass. The model is constructed by imposing the flavor-dependent twisted boundary condition (TBC) on the three-flavor Polyakov-loop extended Nambu-Jona-Lasinio model. In the model, the 3 symmetry is preserved below some temperature Tc, but spontaneously broken above Tc. Dynamics of the simple model is similar to that of the original PNJL model without the TBC, indicating that the 3 symmetry is a good concept. We also investigate the interplay between the 3 symmetry and the emergence of the quarkyonic phase.

symmetry

We propose a simple model with the 3 symmetry in order to answer whether the symmetry is a good concept in QCD with light quark mass. The model is constructed by imposing the flavor-dependent twisted boundary condition (TBC) on the three-flavor Polyakov-loop extended Nambu-Jona-Lasinio model. In the model, the 3 symmetry is preserved below some temperature Tc, but spontaneously broken above Tc. Dynamics of the simple model is similar to that of the original PNJL model without the TBC, indicating that the 3 symmetry is a good concept. We also investigate the interplay between the 3 symmetry and the emergence of the quarkyonic phase.