Goldstone boson currents in a kaon condensed CFL phase

We study the stability of the kaon condensed color-flavor locked (CFL) phase of dense quark matter with regard to the formation of a non-zero Goldstone boson current. In the kaon condensed phase there is an electrically charged fermion which becomes gapless near \mu_s^(1) \simeq 1.35\Delta and a neutral fermion which becomes gapless near \mu_s^(2)\simeq 1.61\Delta. Here, \mu_s=m_s^2/(2p_F) is the shift in the Fermi energy due to the strange quark mass m_s and \Delta is the gap in the chiral limit. The transition to the gapless phase is continuous at \mu_s^(1) and first order at \mu_s^(2). We find that the magnetic screening masses are real in the regime \mu_s< \mu_s^(2), but some screening masses are imaginary for \mu_s> \mu_s^(2). We show that there is a very weak current instability for \mu_s>\mu_s^(1) and a more robust instability in a small window near \mu_s^(2). We also show that in the Goldstone boson current phase all components of the magnetic screening mass are real. There is a range of values of \mu_s below 2\Delta in which the magnetic gluon screening masses are imaginary but the phase is stable with respect to electrically neutral fluctuations of the gauge field.Comment: 16 page

Meson current in the CFL phase

We study the stability of the color-flavor locked (CFL) phase of dense quark matter with regard to the formation of a non-zero Goldstone boson current. We show that an instability appears in the vicinity of the point $\mu_s=\Delta$ which marks the appearance of gapless fermion modes in the CFL phase. Here, $\mu_s=m_s^2/(2\mu)$ is the shift in chemical potential due to the strange quark mass and $\Delta$ is the gap in the chiral limit. We show that in the Goldstone boson current phase all components of the magnetic screening mass are real. In this work we do not take into account homogeneous kaon condensation. We study the effects of an instanton induced interaction of the magnitude required to suppress kaon condensation.Comment: 15 pages, 5 figures, v2: minor improvements, results unchange

Mass Terms in Effective Theories of High Density Quark Matter

We study the structure of mass terms in the effective theory for quasi-particles in QCD at high baryon density. To next-to-leading order in the $1/p_F$ expansion we find two types of mass terms, chirality conserving two-fermion operators and chirality violating four-fermion operators. In the effective chiral theory for Goldstone modes in the color-flavor-locked (CFL) phase the former terms correspond to effective chemical potentials, while the latter lead to Lorentz invariant mass terms. We compute the masses of Goldstone bosons in the CFL phase, confirming earlier results by Son and Stephanov as well as Bedaque and Sch\"afer. We show that to leading order in the coupling constant $g$ there is no anti-particle gap contribution to the mass of Goldstone modes, and that our results are independent of the choice of gauge.Comment: 22 pages, 4 figure

Instantons in non-Cartesian coordinates

The explicit multi-instanton solutions by 'tHooft and Jackiw, Nohl & Rebbi are generalized to curvilinear coordinates. The idea is that a gauge transformation can notably simplify the expressions obtained after the change of variables. The gauge transform generates a compensating addition to the gauge potential of pseudoparticles. Singularities of the compensating field are irrelevant for physics but may affect gauge dependent quantities.Comment: 10 pages, LaTeX, talk given at Quarks-2000 (Pushkin, Russia) and E.S.Fradkin (Moscow, Russia) conference

A Diagrammatic Approach to Crystalline Color Superconductivity

We present a derivation of the gap equation for the crystalline color superconducting phase of QCD which begins from a one-loop Schwinger-Dyson equation written using a Nambu-Gorkov propagator modified to describe the spatially varying condensate. Some aspects of previous variational calculations become more straightforward when rephrased beginning from a diagrammatic starting point. This derivation also provides a natural base from which to generalize the analysis to include quark masses, nontrivial crystal structures, gluon propagation at asymptotic densities, and nonzero temperature. In this paper, we analyze the effects of nonzero temperature on the crystalline color superconducting phase.Comment: 15 pages. 2 eps figure

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

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