QCD at Finite Density and Color Superconductivity

Brief review of current status of the field.Comment: Invited talk at Lattice 99, Pisa, July 1999. 5 pages, 7 fig

A chiral crystal in cold QCD matter at intermediate densities?

The analogue of Overhauser (particle-hole) pairing in electronic systems (spin-density waves with non-zero total momentum $Q$) is analyzed in finite-density QCD for 3 colors and 2 flavors, and compared to the color-superconducting BCS ground state (particle-particle pairing, $Q$=0). The calculations are based on effective nonperturbative four-fermion interactions acting in both the scalar diquark as well as the scalar-isoscalar quark-hole ('$\sigma$') channel. Within the Nambu-Gorkov formalism we set up the coupled channel problem including multiple chiral density wave formation, and evaluate the resulting gaps and free energies. Employing medium-modified instanton-induced 't Hooft interactions, as applicable around $\mu_q\simeq 0.4$ GeV (or 4 times nuclear saturation density), we find the 'chiral crystal phase' to be competitive with the color superconductor.Comment: 14 pages ReVTeX, including 11 ps-/eps-figure

Multiflavor Correlation Functions in non-Abelian Gauge Theories at Finite Density in two dimensions

We compute vacuum expectation values of products of fermion bilinears for two-dimensional Quantum Chromodynamics at finite flavored fermion densities. We introduce the chemical potential as an external charge distribution within the path-integral approach and carefully analyse the contribution of different topological sectors to fermion correlators. We show the existence of chiral condensates exhibiting an oscillatory inhomogeneous behavior as a function of a chemical potential matrix. This result is exact and goes in the same direction as the behavior found in QCD_4 within the large N approximation.Comment: 28 pages Latex (3 pages added and other minor changes) to appear in Phys.Rev.

Crystalline ground state in chiral Gross-Neveu and Cooper pair models at finite densities

We study the possibility of spatially non-uniform ground state in (1+1)-dimensional models with quartic fermi interactions at finite fermion densities by introducing chemical potential \mu. We examine the chiral Gross-Neveu model and the Cooper pair model as toy models of the chiral symmetry breaking and the difermion pair condensates which are presumed to exist in QCD. We confirm in the chiral Gross-Neveu model that the ground state has a crystalline structure in which the chiral condensate oscillates in space with wave number 2\mu. Whereas in the Cooper pair model we find that the vacuum structure is spatially uniform. Some discussions are given to explain this difference.Comment: 18 pages, REVTeX, 3 eps figure

Spontaneous symmetry breaking in strong-coupling lattice QCD at high density

We determine the patterns of spontaneous symmetry breaking in strong-coupling lattice QCD in a fixed background baryon density. We employ a next-nearest-neighbor fermion formulation that possesses the SU(N_f)xSU(N_f) chiral symmetry of the continuum theory. We find that the global symmetry of the ground state varies with N_f and with the background baryon density. In all cases the condensate breaks the discrete rotational symmetry of the lattice as well as part of the chiral symmetry group.Comment: 10 pages, RevTeX 4; added discussion of accidental degeneracy of vacuum after Eq. (35

BCS vs Overhauser pairing in dense (2+1)d QCD

We compare the BCS and Overhauser effect as competing mechanisms for the destabilization of the quark Fermi surface at asymptotically large chemical potential, for the special case of 2 space and 1 time dimension. We use the framework of perturbative one-gluon exchange, which dominates the pairing at $\mu/g^2\gg 1$. With screening in matter, we show that in the weak coupling limit the Overhauser effect can compete with the BCS effect only for a sufficiently large number of colors. Both the BCS and the Overhauser gaps are of order $g^{4}/\mu$ in Landau gauge.Comment: 10 pages, no figur

Phases of QCD at High Baryon Density

We review recent work on the phase structure of QCD at very high baryon density. We introduce the phenomenon of color superconductivity and discuss how the quark masses and chemical potentials determine the structure of the superfluid quark phase. We comment on the possibility of kaon condensation at very high baryon density and study the competition between superfluid, density wave, and chiral crystal phases at intermediate density.Comment: 15 pages. To appear in the proceedings of the ECT Workshop on Neutron Star Interiors, Trento, Italy, June 200

Views of the Chiral Magnetic Effect

My personal views of the Chiral Magnetic Effect are presented, which starts with a story about how we came up with the electric-current formula and continues to unsettled subtleties in the formula. There are desirable features in the formula of the Chiral Magnetic Effect but some considerations would lead us to even more questions than elucidations. The interpretation of the produced current is indeed very non-trivial and it involves a lot of confusions that have not been resolved.Comment: 19 pages, no figure; typos corrected, references significantly updated, to appear in Lect. Notes Phys. "Strongly interacting matter in magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Ye

Color Superconductivity in Compact Stars

After a brief review of the phenomena expected in cold dense quark matter, color superconductivity and color-flavor locking, we sketch some implications of recent developments in our understanding of cold dense quark matter for the physics of compact stars. We give a more detailed summary of our recent work on crystalline color superconductivity and the consequent realization that (some) pulsar glitches may originate in quark matter.Comment: 19 pages. 2 figures. To appear in the proceedings of the ECT Workshop on Neutron Star Interiors, Trento, Italy, June 2000. Shorter versions contributed to the proceedings of Strong and Electroweak Matter 2000, Marseille, France, June 2000 and to the proceedings of Strangeness 2000, Berkeley, CA, July 2000. KR was the speaker at all three meeting

Superdense Matter

We review recent work on the phase structure of QCD at very high baryon density. We introduce the phenomenon of color superconductivity and discuss the use of weak coupling methods. We study the phase structure as a function of the number of flavors and their masses. We also introduce effective theories that describe low energy excitations at high baryon density. Finally, we study the possibility of kaon condensation at very large baryon density.Comment: 13 pages, talk at ICPAQGP, Jaipur, India, Nov. 26-30, 2001; to appear in the proceeding