Viscosity bound for anisotropic superfluids with dark matter sector

The shear viscosity to the entropy density ratio eta/s of the anisotropic superfluid has been calculated by means of the gauge/gravity duality in the presence of the dark matter sector. The dark matter has been described by theYang-Mills field analogous to the one describing the visible matter sector, and it is assumed to interact with the visible field with coupling constant alpha. Close to the superfluid transition temperature (T-c), the analytical solution has been given up to the leading order in a symmetry breaking parameter and the ratio of the gravitational constant and Yang-Mils coupling. The tensor element of ratio eta/s remains unaffected by the darkmatter for the viscosity tensor in the plane perpendicular to the symmetry breaking direction (here, yz). The temperature dependence and the linear correction in (1 - alpha) in the plane containing this direction (here, xy) was also revealed. The correction linearly vanishes for temperature tending to the critical one T -> T-c.