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Shear viscosity from kaon condensation in color-flavor-locked quark matter

We calculate the kaonic contribution to the shear viscosity of quark matter in the kaon-condensed color-flavor locked phase (CFL-K0). This contribution comes from a light pseudo-Goldstone boson which arises from the spontaneous breaking of the flavor symmetry by the kaon condensate. The other contribution, from the exactly massless superfluid 'phonon", has been calculated previously. We specialize to a particular form of the interaction lagrangian, parameterized by a single coupling. We find that if we make reasonable guesses for the values of the parameters of the effective theory, the kaons have a much smaller shear viscosity than the superfluid phonons, but also a much shorter mean free path, so they could easily provide the dominant contribution to the shear viscosity of CFL-K0 quark matter in a neutron star in the temperature range 0.01 to 1 MeV (10^8 to 10^10 K).