Effective Description of QCD at Very High Densities

Abstract

We describe the effective lagrangian approach to the color superconductivity. The effective description that arises if one considers only the leading terms in the expansion for very high densities is particularly simple. It is based on a lagrangian whose effective fermion fields are velocity-dependent; moreover strong interactions do not change quark velocity and the effective lagrangian does not contain spin matrices. All these features render the effective theory similar to the Heavy Quark Effective Theory, which is the limit of Quantum ChromoDynamics for infinite quark masses. For this reason one can refer to the effective lagrangian at high density as the High Density Effective Theory (HDET). In some cases HDET results in analytical, though approximate, relations that are particularly simple to handle. After a pedagogical introduction, several topics are considered. They include the treatment of the Color-Flavor-Locking and the 2SC model, with evaluation of the gap parameters by the Nambu-Gorkov equations, approximate dispersion laws for the gluons and calculations of the Nambu-Goldstone Bosons properties. We also discuss the effective lagrangian for the crystalline color superconductive (LOFF) phase and we give a description of the phonon field related to the breaking of the rotational and translational invariance. Finally a few astrophysical applications of color superconductivity are discussed.

85 pages, 11 figures, v3: minor grammatical changes, some misprints corrected, Fig, 4.1 replaced. This version will appear in Rivista del Nuovo Cimento

References in corpus (14)

• The Condensed Matter Physics of QCD
• Modeling Quintessential Inflation
• Color-flavor locked strangelets
• A Diagrammatic Approach to Crystalline Color Superconductivity
• Opening the Crystalline Color Superconductivity Window
• The Influence of an External Chromomagnetic Field on Color Superconductivity
• Effective Field Theory for the Crystalline Colour Superconductive Phase of QCD
• The Glueball sector of two-flavor Color Superconductivity
• Effective gluon interactions in the Colour Superconductive Phase of two flavor QCD
• Transport theory for a two-flavor color superconductor
• Implications of a New Effective Chiral Meson Lagrangian
• Aspects of Color Superconductivity
• Chromomagnetic Catalysis of Chiral Symmetry Breaking and Color Superconductivity
• Effective Theory for QCD in the LOFF Phase

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• Color neutral 2SC phase of cold and dense quark matter in the presence of constant magnetic fields
• Ginzburg-Landau approach to the three flavor LOFF phase of QCD
• Phase Structure of 2-Flavor Quark Matter: Heterogeneous Superconductors
• Non-Fermi Liquid Effects in QCD at High Density
• Deconfinement and color superconductivity in cold neutron stars
• Towards A Holographic Model of Color Superconductivity
• Finite size effects in the Gross-Neveu model with isospin chemical potential
• How do chiral condensates affect color superconducting quark matter under charge neutrality constraints?
• Self-consistent evaluation of quark masses in three flavor crystalline color superconductivity
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• Aspects of the Color Flavor Locking phase of QCD in the Nambu-Jona Lasinio approximation
• Quark and pion condensation in a chromomagnetic background field
• Single-flavour and two-flavour pairing in three-flavour quark matter
• Collective modes in the color flavor locked phase
• Chiral symmetry breaking, color superconductivity, and the equation of state for magnetized strange quark matter
• Quasi-particle Specific Heats for the Crystalline Color Superconducting Phase of QCD
• A diagrammatic derivation of the meson effective masses in the neutral color-flavor-locked phase of Quantum Chromodynamics
• Unusual condensates in quark and atomic systems
• LOFF and breached pairing with cold atoms
• Symmetry energy in cold dense matter
• Effective Theories of Dense and Very Dense Matter
• Some aspects of color superconductivity: an introduction
• Magnetic properties of the Larkin-Ovchinnikov-Fulde-Ferrell superconducting phase
• Effective Fields in Dense Quantum Chromodynamics
• Inhomogeneous color superconductivity and the cooling of compact stars
• A study of meson condensation and of the QCD critical line
• High density effective theory results for two and three massive flavors color-suoerconductivity