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. 
Andreas Gerhold, Thomas Schaefer (North Carolina State University) and   Andrei Kryjevski (Indiana University)