Goldstone boson currents in a kaon condensed color-flavor locked 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 nonzero Goldstone boson current. In the kaon condensed phase there is an electrically charged fermion which becomes gapless near μs(1)≅1.35Δ and a neutral fermion which becomes gapless near μs(2)≅1.61Δ. Here, μs=ms2/(2pF) is the shift in the Fermi energy due to the strange quark mass ms and Δ is the gap in the chiral limit. The transition to the gapless phase is continuous at μs(1) and first order at μs(2). We find that the magnetic screening masses are real in the regime μs<μs(2), but some screening masses are imaginary for μs>μs(2). We show that there is a very weak current instability for μs>μs(1) and a more robust instability in a small window near μs(2). We show that in the Goldstone boson current phase all components of the magnetic screening mass are real. There is a range of values of μs below 2Δ in which the magnetic gluon screening masses are imaginary but the phase is stable with respect to electrically neutral fluctuations of the gauge field