Viscosity bound for anisotropic superfluids with dark matter sector

Abstract

The shear viscosity to the entropy density ratio η/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 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 α. Close to the superfluid transition temperature (Tc) 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 η/s remains unaffected by the 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 − α) in the plane containing this direction (here xy) was also revealed. The correction linearly vanishes for temperature tending to the critical one T → Tc.

Non-Abelian vortices in holographic superconductors

“…We will not perform this analysis in this paper and content ourselves with the meta-stability of this solution implied by the energy arguments. A similar result was derived in [25] when considering vortices in the presence of an additional U (1) gauge sector.…”

“…This was recently interpreted as a dark sector in holographic vortex applications [25]. However, it seems plausible that coupling of both scalars to the original U (1) gauge field might be sufficient to find non-Abelian vortex solutions.…”

Holographic Superconductivity in the Presence of Dark Matter: Basic Issues

“…The other strong coupling effects include the upward curvature seen in the temperature dependence of the upper critical field calculated via AdS/CFT correspondence [15][16][17][18][19]. It leads to the value of zero temperature magnetic field higher than the estimate based on the equation [20]:…”

“…Working in the probe limit we have found that dark matter sector affects various properties of the holographic superconductors depending on their symmetry and other details. In particular the superconducting transition temperature T c of the s-wave superconductor with dark matter (DM) is modified as T = T c /α 1/6 , while in the Maxwell vector p-wave holographic superconductor with dark matter sector and for real components of the vector field gives us the same description of the phase transitions as the s-wave model [15][16][17][18][19]. It is worth noting the dependence of the superconducting transition temperature T c on the charge density ρ, which is T c ∝ ρ 1/3 .…”

“…Similarly, the concept of dark matter requires a lot of theoretical studies and observations before it will be properly and completely understood. Our work [15][16][17][18][19] is directed towards better understanding of both: strongly coupled superconductors and seemingly omnipresent, but still illusory dark matter.…”