Viscosity bound for anisotropic superfluids with dark matter sector

TL;DR

This paper investigates how dark matter influences the shear viscosity to entropy density ratio in anisotropic superfluids using gauge/gravity duality, revealing directional dependence and temperature-related corrections near the transition.

Contribution

It provides an analytical study of dark matter effects on viscosity ratios in anisotropic superfluids within a holographic framework, including temperature dependence and directional effects.

Findings

The viscosity ratio in the plane perpendicular to symmetry breaking is unaffected by dark matter.

A linear correction in the dark matter coupling appears in the viscosity ratio within the symmetry breaking plane.

The correction vanishes as temperature approaches the critical temperature.

Abstract

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 {\it dark matter} sector. The {\it dark matter} has been described by the Yang-Mills field analogous to the one describing 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 {\it dark matter} 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 $T\rightarrow T_c$.