Dimensional reduction and a Z(3) symmetric model

We present first results from a numerical investigation of a Z(3) symmetric model based on dimensional reduction.Comment: Talk presented at XXI International Symposium on Lattice Field Theory lattice2003(Non-zero temperature and density

Thermodynamics of the PNJL model with nonzero baryon and isospin chemical potentials

We have extended the Polyakov-Nambu-Jona-Lasinio (PNJL) model for two degenerate flavours to include the isospin chemical potential ($\mu_I$). All the diagonal and mixed derivatives of pressure with respect to the quark number (proportional to baryon number) chemical potential ($\mu_0$) and isospin chemical potential upto sixth order have been extracted at $\mu_0 = \mu_I = 0$. These derivatives give the generalized susceptibilities with respect to quark and isospin numbers. Similar estimates for the flavour diagonal and off-diagonal susceptibilities are also presented. Comparison to Lattice QCD (LQCD) data of some of these susceptibilities for which LQCD data are available, show similar temperature dependence, though there are some quantitative deviations above the crossover temperature. We have also looked at the effects of instanton induced flavour-mixing coming from the $U_A(1)$ chiral symmetry breaking 't Hooft determinant like term in the NJL part of the model. The diagonal quark number and isospin susceptibilities are completely unaffected. The off-diagonal susceptibilities show significant dependence near the crossover. Finally we present the chemical potential dependence of specific heat and speed of sound within the limits of chemical potentials where neither diquarks nor pions can condense.Comment: 15 pages, 7 figures, Added discussions and references, version to appear in Phys. Rev.

Numerical solution of the color superconductivity gap in a weak coupling constant

We present the numerical solution of the full gap equation in a weak coupling constant $g$. It is found that the standard approximations to derive the gap equation to the leading order of coupling constant are essential for a secure numerical evaluation of the logarithmic singularity with a small coupling constant. The approximate integral gap equation with a very small $g$ should be inverted to a soft integral equation to smooth the logarithmic singularity near the Fermi surface. The full gap equation is solved for a rather large coupling constant $g\ge 2.0$. The approximate and soft integral gap equations are solved for small $g$ values. When their solutions are extrapolated to larger $g$ values, they coincide the full gap equation solution near the Fermi surface. Furthermore, the analytical solution matches the numerical one up to the order one O(1). Our results confirm the previous estimates that the gap energy is of the order tens to 100 MeV for the chemical potential $\mu\le 1000$ MeV. They also support the validity of leading approximations applied to the full gap equation to derive the soft integral gap equation and its analytical solution near the Fermi surface.Comment: 7 pages+ 6 figs, Stanford, Frankfurt and Bethlehe

Another weak first order deconfinement transition: three-dimensional SU(5) gauge theory

We examine the finite-temperature deconfinement phase transition of (2+1)-dimensional SU(5) Yang-Mills theory via non-perturbative lattice simulations. Unsurprisingly, we find that the transition is of first order, however it appears to be weak. This fits naturally into the general picture of "large" gauge groups having a first order deconfinement transition, even when the center symmetry associated with the transition might suggest otherwise.Comment: 17 pages, 8 figure

Color superconductivity in weak coupling

We derive perturbatively the gap equations for a color-superconducting condensate with total spin J=0 in dense QCD. At zero temperature, we confirm the results of Son for the dependence of the condensate on the coupling constant, and compute the prefactor to leading logarithmic accuracy. At nonzero temperature, we find that to leading order in weak coupling, the temperature dependence of the condensate is identical to that in BCS-like theories. The condensates for total spin J=1 are classified; to leading logarithmic accuracy these condensates are of the same order as those of spin J=0.Comment: 30 pages, 3 figures, RevTeX, epsf and psfig style files require

Small, Dense Quark Stars from Perturbative QCD

As a model for nonideal behavior in the equation of state of QCD at high density, we consider cold quark matter in perturbation theory. To second order in the strong coupling constant, $\alpha_s$, the results depend sensitively on the choice of the renormalization mass scale. Certain choices of this scale correspond to a strongly first order chiral transition, and generate quark stars with maximum masses and radii approximately half that of ordinary neutron stars. At the center of these stars, quarks are essentially massless.Comment: ReVTeX, 5 pages, 3 figure

Possibility of spontaneous parity violation in hot QCD

We suggest that for QCD in the limit of a large number of colors, N, the axial U(1) symmetry of massless quarks is effectively restored at the deconfining=chiral phase transition. If the deconfining transition is of second order, then the chiral transition is weakly first order. In this case, metastable states in which parity is spontaneously broken appear at temperatures below the phase transition. The production of these metastable states would have dramatic signatures, including enhanced production of eta and eta' mesons, which can decay through parity violating decay processes such as eta -> pi^0 pi^0, and global parity odd asymmetries for charged pions. Using a nonlinear sigma model, in QCD these metastable states only appear rather near the phase transition.Comment: 4 pages, REVTe

QCD and the Chiral Critical Point

As an extension of $QCD$, consider a theory with ``$2+1$'' flavors, where the current quark masses are held in a fixed ratio as the overall scale of the quark masses is varied. At nonzero temperature and baryon density it is expected that in the chiral limit the chiral phase transition is of first order. Increasing the quark mass from zero, the chiral transition becomes more weakly first order, and can end in a chiral critical point. We show that the only massless field at the chiral critical point is a sigma meson, with the universality class that of the Ising model. Present day lattice simulations indicate that $QCD$ is (relatively) near to the chiral critical point.Comment: 7 pages + 2 figures, BNL-GGP-

PNJL model with a Van der Monde term

We extend the Polyakov-Nambu-Jona-Lasinio (PNJL) model for two degenerate flavours by including the effect of the SU(3) measure with a Van der Monde (VdM) term. This ensures that the Polyakov loop always remains in the domain [0,1]. The pressure, energy density, specific heat, speed of sound and conformal measure show small or negligible effects from this term. However various quark number and isospin susceptibilities are all found to approach their respective ideal gas limits around 2 $T_c$. We compare our methods with other similar approaches in PNJL model and also present a quantitative comparison with Lattice QCD data.Comment: 12 pages, 8 eps figures; extended discussion and reference added; accepted in Phys. Rev.