Shear viscosity of two-flavor inhomogenous color superconducting quark matter

We present the first calculation of the shear viscosity for two-flavor plane wave (FF) color superconducting quark matter. This is a member of the family of crystalline color superconducting phases of dense quark matter that may be present in the cores of neutron stars. The paired quarks in the FF phase feature gapless excitations on surfaces of crescent-shaped blocking regions in momentum space and participate in transport. We calculate their contribution to the shear viscosity. We also note that the transverse t(1), t(2), t(3) gluons which are undamped in the 2SC lead to dynamic screening in the FF phase. The exchange of these gluons is the most important mechanism of the scattering of the paired quarks. We find that the shear viscosity of the paired quarks is roughly a factor of 100 smaller compared to the shear viscosity of unpaired quark matter even though their spectrum is ungapped. Therefore in the two-flavor FF phase, the unpaired quarks and the electrons give the shear viscosity of the two-flavor FF phase to a very good approximation. Our results may have implications for the damping of r-modes in rapidly rotating, cold neutron stars.