Viscosity of holographic fluid in the presence of dark matter sector

TL;DR

This paper investigates how dark matter influences the shear and Hall viscosities of a holographic fluid using gauge/gravity duality, revealing that dark matter coupling affects Hall viscosity but not shear viscosity.

Contribution

It introduces a holographic model coupling dark matter sector with a gravitational system and calculates viscosities, highlighting the linear dependence of Hall viscosity on dark matter coupling.

Findings

Shear viscosity remains unaffected by dark matter coupling.

Hall viscosity linearly depends on the dark matter coupling constant.

Scalar field condensation induces parity violation.

Abstract

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 {\it 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 provides the parity violating term. Both shear and Hall viscosities have been calculated and their dependence on $\alpha$ - the coupling constant between matter and {\it dark matter} sectors has been studied. To the lowest order in the derivative expansion and perturbation in $\alpha$, the shear viscosity is not influenced by the {\it dark matter}, while the Hall component linearly depends on $\alpha$.