Viscosity of holographic fluid in the presence of dark matter sector

Based on the gauge/gravity correspondence, the hydrodynamic response coefficients, shear and Hall viscosities, have been studied. The holographic model of Einstein-Maxwell-AdS (3+1)-dimensional system additionally coupled with the another gauge field mimicking the dark matter sector, as well as, gravitational Chern-Simons term bounded with a dynamical scalar field, were taken into account. Condensation of the scalar field in the presence of the deformation chemical potential for the dark matter gauge field provide the parity violating terms. Both shear and Hall viscosities have been calculated and their dependence on α — the coupling constant between matter and dark matter sectors has been studied. To the lowest order in the derivative expansion and perturbation in α, the shear viscosity is not influenced by the dark matter, while the Hall component linearly depends on α.