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The Shear Viscosity in Anisotropic Phases

Sachin Jain, Rickmoy Samanta, Sandip P. Trivedi

TL;DR

The paper shows that in holographic models of anisotropic, strongly coupled fluids, certain shear-viscosity components can violate the KSS bound parametrically when anisotropy dominates the temperature. By constructing various translationally invariant anisotropic backgrounds (dilaton/axion profiles and magnetic fields) and analyzing spin-1 metric perturbations, they derive a general horizon-based relation η_{xz}/s = (1/4π) (g_{xx}/g_{zz})|_{u_h}, which ties bound-violating behavior to horizon geometry. A unifying mechanism is provided via Kaluza-Klein reduction, linking the viscosity problem to horizon conductivities of emergent gauge fields, and this framework generalizes to higher-dimensional reductions. The results suggest that similar small-viscosity components could arise in real-world strongly coupled anisotropic fluids, with implications for QCD, neutron stars, and cold-atom experiments.

Abstract

We construct anisotropic black brane solutions and analyse the behaviour of some of their metric perturbations. These solutions correspond to field theory duals in which rotational symmetry is broken due an externally applied, spatially constant, force. We find, in several examples, that when the anisotropy is sufficiently big compared to the temperature, some components of the viscosity tensor can become very small in units of the entropy density, parametrically violating the KSS bound. We obtain an expression relating these components of the viscosity, in units of the entropy density, to a ratio of metric components at the horizon of the black brane. This relation is generally valid, as long as the forcing function is translationally invariant, and it directly connects the parametric violation of the bound to the anisotropy in the metric at the horizon. Our results suggest the possibility that such small components of the viscosity tensor might also arise in anisotropic strongly coupled fluids found in nature.

The Shear Viscosity in Anisotropic Phases

TL;DR

The paper shows that in holographic models of anisotropic, strongly coupled fluids, certain shear-viscosity components can violate the KSS bound parametrically when anisotropy dominates the temperature. By constructing various translationally invariant anisotropic backgrounds (dilaton/axion profiles and magnetic fields) and analyzing spin-1 metric perturbations, they derive a general horizon-based relation η_{xz}/s = (1/4π) (g_{xx}/g_{zz})|_{u_h}, which ties bound-violating behavior to horizon geometry. A unifying mechanism is provided via Kaluza-Klein reduction, linking the viscosity problem to horizon conductivities of emergent gauge fields, and this framework generalizes to higher-dimensional reductions. The results suggest that similar small-viscosity components could arise in real-world strongly coupled anisotropic fluids, with implications for QCD, neutron stars, and cold-atom experiments.

Abstract

We construct anisotropic black brane solutions and analyse the behaviour of some of their metric perturbations. These solutions correspond to field theory duals in which rotational symmetry is broken due an externally applied, spatially constant, force. We find, in several examples, that when the anisotropy is sufficiently big compared to the temperature, some components of the viscosity tensor can become very small in units of the entropy density, parametrically violating the KSS bound. We obtain an expression relating these components of the viscosity, in units of the entropy density, to a ratio of metric components at the horizon of the black brane. This relation is generally valid, as long as the forcing function is translationally invariant, and it directly connects the parametric violation of the bound to the anisotropy in the metric at the horizon. Our results suggest the possibility that such small components of the viscosity tensor might also arise in anisotropic strongly coupled fluids found in nature.

Paper Structure

This paper contains 17 sections, 139 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Brief Review of The System With One Dilaton
  3. More Details On The Calculation Of Viscosity
  4. Additional examples with anisotropy
  5. Anisotropic solution in two dilaton gravity system
  6. Viscosity in the Presence of a Uniform Magnetic Field
  7. The Dilaton-Axion System
  8. The two Axion-one Dilaton System
  9. Kaluza Klein Reduction
  10. The Dimensionally Reduced Theory
  11. The Viscosity To Entropy Ratio
  12. Generalisation To Case with Additional Directions
  13. Conclusion
  14. Acknowledgements
  15. Numerical interpolation from the near horizon $AdS_3 \times R \times R$ to asymptotic $AdS_5$,
  16. ...and 2 more sections

Figures (2)

  • Figure 1: Picture showing flow of fluid enclosed between two parallel plates separated along the $z$-direction.
  • Figure 2: Log-log plot showing the numerical interpolation of near horizon $AdS_3 \times R \times R$ to asymptotic $AdS_5$ , with $\rho_{1}=1$ , $\rho_{2}=1$.