The shear viscosity of holographic superfluids

TL;DR

This work analyzes η/s for holographic superfluids across s wave, p wave, and p plus ip wave classes. Using tensor mode perturbations and holographic renormalization, it establishes the universal value η/s = 1/(4π) for s wave and for the p wave tensor mode η^{2323}/s in d ≥ 4, while highlighting that η^{1212} and the p plus ip case resist the standard analysis due to couplings with Yang–Mills perturbations. It also demonstrates that η does not exhibit a singular behavior at the superconducting phase transition, offering insights into dynamic critical phenomena in holographic contexts. The results underscore both the reach and the limits of current tensor-mode techniques in anisotropic holographic systems and point to directions for fully backreacted or coupled analyses to resolve open coefficients.

Abstract

We study the ratio of the shear viscosity to the entropy density for various holographic superfluids. For the s-wave case, the ratio has the universal value 1/(4pi) as in various holographic models. For the p-wave case, there are two shear viscosity coefficients because of the anisotropic boundary spacetime, and one coefficient has the universal value. For the (p+ip)-wave case, the existing technique is not applicable since there is no tensor mode of metric perturbations which decouples from Yang-Mills perturbations. Our results indicate that the shear viscosity does not show a singular behavior at the critical point for holographic superfluids.