A Strongly Coupled Anisotropic Fluid From Dilaton Driven Holography

TL;DR

This work constructs and analyzes a dilaton-driven holographic model of a strongly coupled anisotropic fluid by introducing a linearly varying boundary dilaton φ = ρ z in AdS$_5$ gravity. The backreacted black brane exhibits a high-ρ/low-T regime governed by an AdS$_4$ × R near-horizon attractor, yielding an IR fixed point with reduced rotational symmetry. The authors compute transport properties, showing the spin-2 viscosity saturates η$_∥$/s = 1/(4π) while the spin-1 component η$_⊥$/s scales as ∝ T$^2$/ρ$^2$ and can vanish at extremality, violating the KSS bound in that sector but without apparent instabilities. They develop a systematic first-order anisotropic fluid mechanics, demonstrate a frictional flow between plates sensitive to orientation, and discuss string embeddings, finding instabilities in certain IIB compactifications near extremality. Overall, the paper links horizon geometry, QNMs, and derivative-ordered fluid dynamics to reveal novel anisotropic transport in strongly coupled holographic systems and highlights the conditions under which small viscosity can be achieved without destabilizing the system.

Abstract

We consider a system consisting of $5$ dimensional gravity with a negative cosmological constant coupled to a massless scalar, the dilaton. We construct a black brane solution which arises when the dilaton satisfies linearly varying boundary conditions in the asymptotically $AdS_5$ region. The geometry of this black brane breaks rotational symmetry while preserving translational invariance and corresponds to an anisotropic phase of the system. Close to extremality, where the anisotropy is big compared to the temperature, some components of the viscosity tensor become parametrically small compared to the entropy density. We study the quasi normal modes in considerable detail and find no instability close to extremality. We also obtain the equations for fluid mechanics for an anisotropic driven system in general, working upto first order in the derivative expansion for the stress tensor, and identify additional transport coefficients which appear in the constitutive relation. For the fluid of interest we find that the parametrically small viscosity can result in a very small force of friction, when the fluid is enclosed between appropriately oriented parallel plates moving with a relative velocity.

Figures (17)

• Figure 1: Numerical interpolation of near horizon $AdS_4 \times R$ to asymptotic $AdS_5$, for the metric coefficients $A(u),\,B(u)$ with $\rho=1$ and $c_1=2$.
• Figure 2: Numerical interpolation of near horizon $AdS_4 \times R$ to asymptotic $AdS_5$, for the metric coefficient $C(u)$ with $\rho=1$ and $c_1=2$.
• Figure 3: QNM plot for spin 2 mode for $\frac{q}{\rho}=0,\,2$, with $\vec{q}$ along $z$ direction.
• Figure 4: QNM plots for spin 1 mode with $\frac{q}{\rho}=0,2$ with $\vec{q}$ along $z$ direction
• Figure 5: QNM plot for spin 0 mode with $\frac{q}{\rho}=0,\,\sqrt{2}$ for $Z_0^{(1)}(v)$ with $\vec{q}$ along $z$ direction