Robert D. Pisarski

Phases of cold, dense quarks at large N(c)

Abstract In the limit of a large number of colors, N c , we suggest that gauge theories can exhibit several distinct phases at nonzero temperature and quark density. Two are familiar: a cold, dilute phase of confined hadrons, where the pressure is ∼1, and a hot phase of deconfined quarks and gluons, with pressure ∼ N c 2 . When the quark chemical potential μ ∼ 1 , the deconfining transition temperature, T d , is independent of μ . For T T d , as μ increases above the mass threshold, baryons quickly form a dense phase where the pressure is ∼ N c . As illustrated by a Skyrme crystal, chiral symmetry can be both spontaneously broken, and then restored, in the dense phase. While the pressure is ∼ N c , like that of (non-ideal) quarks, the dense phase is still confined, with interactions near the Fermi surface those of baryons, and not of quarks. Thus in the chirally symmetric region, baryons near the Fermi surface are parity doubled. We suggest possible implications for the phase diagram of QCD.

Quark gluon plasma as a condensate of SU(3) Wilson lines

Effective theories for the thermal Wilson line are constructed in an SU(N) gauge theory at nonzero temperature. I propose that the order of the deconfining phase transition for Z(N) Wilson lines is governed by the behavior of SU(N) Wilson lines. In a mean field theory, the free energy in the deconfined phase is controlled by the condensate for Z(N) Wilson lines. Numerical simulations on the lattice, and the mean field theory for Z(3) Wilson lines, suggest that about any finite temperature transition in QCD, the dominant correlation length increases by a large, uniform factor, of order five.

Hadron production in ultra-relativistic nuclear collisions: Quarkyonic matter and a triple point in the phase diagram of QCD

We argue that features of hadron production in relativistic nuclear collisions, mainly at CERN-SPS energies, may be explained by the existence of three forms of matter: Hadronic Matter, Quarkyonic Matter, and a Quark-Gluon Plasma. We suggest that these meet at a triple point in the QCD phase diagram. Some of the features explained, both qualitatively and semi-quantitatively, include the curve for the decoupling of chemical equilibrium, along with the non-monotonic behavior of strange particle multiplicity ratios at center of mass energies near 10 GeV. If the transition(s) between the three phases are merely crossover(s), the triple point is only approximate.

Quarkyonic Chiral Spirals

Abstract We consider the formation of chiral density waves in Quarkyonic matter, which is a phase where cold, dense quarks experience confining forces. We model confinement following Gribov and Zwanziger, taking the gluon propagator, in Coulomb gauge and momentum space, as ∼ 1 / ( p → 2 ) 2 . We assume that the number of colors, N c , is large, and that the quark chemical potential, μ , is much larger than renormalization mass scale, Λ QCD . To leading order in 1 / N c and Λ QCD / μ , a gauge theory with N f flavors of massless quarks in 3 + 1 dimensions naturally reduces to a gauge theory in 1 + 1 dimensions, with an enlarged flavor symmetry of SU ( 2 N f ) . Through an anomalous chiral rotation, in two dimensions a Fermi sea of massless quarks maps directly onto the corresponding theory in vacuum. A chiral condensate forms locally, and varies with the spatial position, z , as 〈 ψ ¯ exp ( 2 i μ z γ 0 γ z ) ψ 〉 . Following Schon and Thies, we term this two-dimensional pion condensate a (Quarkyonic) chiral spiral. Massive quarks also exhibit chiral spirals, with the magnitude of the oscillations decreasing smoothly with increasing mass. The power law correlations of the Wess–Zumino–Novikov–Witten model in 1 + 1 dimensions then generate strong infrared effects in 3 + 1 dimensions.

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

Deconfining Phase Transition as a Matrix Model of Renormalized Polyakov Loops

{\ensuremath{\alpha}}_{s},

Color superconductivity in weak coupling

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.

Effective theory of Wilson lines and deconfinement

We discuss how to extract renormalized loops from bare Polyakov loops in

Pionic measures of parity and CP violation in high-energy nuclear collisions

\mathrm{SU}(N)

Baryons and the phase diagram for a large number of colors and flavors

lattice gauge theories at nonzero temperature. Single loops in an irreducible representation are multiplicatively renormalized, without mixing, through mass renormalization. The values of renormalized loops in the four lowest representations of