Effective Fields in Dense Quantum Chromodynamics

In the high density, low temperature limit, Quantum Chromodynamics exhibits a transition to phases characterized by color superconductivity and energy gaps in the fermion spectra. We review some fundamental results obtained in this area and in particular we describe the low energy effective lagrangian describing the motion of the quasi-particles in the high density medium (High Density Effective Theory).Comment: 17 pages, Invited review talk at Workshop on Quark Gluon Plasma and Relativistic Heavy Ions, Frascati, Italy, 14-18 Jan 200

QCD, hadrons and beyond

I give a summary of Section E of the sixth edition of the Conference "Quark confinement and the hadron spectrum". Papers were presented on different subjects, from spectroscopy, including pentaquarks and hadron structure, to new physics effects (non commutative field theories, supersymmetry and extra dimensions) and the problem of color confinement, both in ordinary Yang-Mills models and in supersymmetric Yang-Mills.Comment: Summary talk of Section E for the Conference "Quark Confinement and the Hadron Spectrum VI", Villasimius, Cagliari, Italy, September 21-25, 200

Enforced neutrality and color-flavor unlocking in the three-flavor Polyakov-loop NJL model

We study how the charge neutrality affects the phase structure of three-flavor PNJL model. We point out that, within the conventional PNJL model at finite density the color neutrality is missing because the Wilson line serves as an external ``colored'' field coupled to dynamical quarks. In this paper we heuristically assume that the model may still be applicable. To get color neutrality one has then to allow non vanishing color chemical potentials. We study how the quark matter phase diagram in $(T,m_s^2/\mu)$-plane is affected by imposing neutrality and by including the Polyakov loop dynamics. Although these two effects are correlated in a nonlinear way, the impact of the Polyakov loop turns out to be significant in the $T$ direction, while imposing neutrality brings a remarkable effect in the $m_s^2/\mu$ direction. In particular, we find a novel unlocking transition, when the temperature is increased, even in the chiral SU(3) limit. We clarify how and why this is possible once the dynamics of the colored Polyakov loop is taken into account. Also we succeed in giving an analytic expression for $T_c$ for the transition from two-flavor pairing (2SC) to unpaired quark matter in the presence of the Polyakov loop.Comment: 11 pages, REVTex4, 10 eps figures; v2: added two notes, added a reference; version to appear in Phys. Rev.

On the Hamilton's isoperimetric ratio in complete Riemannian manifolds of finite volume

We contribute to an original problem studied by Hamilton and others, in order to understand the behaviour of maximal solutions of the Ricci flow both in compact and non-compact complete orientable Riemannian manifolds of finite volume. The case of dimension two has peculiarities, which force us to use different ideas from the corresponding higher dimensional case. We show the existence of connected regions with a connected complementary set (the so-called "separating regions"). In dimension higher than two, the associated problem of minimization is reduced to an auxiliary problem for the isoperimetric profile. This is possible via an argument of compactness in geometric measure theory. Indeed we develop a definitive theory, which allows us to circumvent the shortening curve flow approach of previous authors at the cost of some applications of geometric measure theory and Ascoli-Arzela's Theorem.Comment: Example 5.4 is new; Theorem 4.5 is reformulated; 29 pages; 7 figure

Resummed one-loop gluonic contributions to the color superconducting color charge density vanish

It is shown that gluonic corrections to the tadpole diagrams vanish in the 2SC and CFL phases at the order where one might have expected NLO corrections. This implies that the gluonic part of the color charge density is negligible at the order of our computation. This statement remains true after inclusion of the gluon vertex correction and contributions from Nambu-Goldstone bosons.Comment: 9 pages, 3 figures, REVTeX4; title modified, comments about gauge independence added, accepted for publication in Phys. Rev.