[Paper Review] Holographic transports and stability in anisotropic linear axion model

Xian-Hui Ge, Yi Ling+2 more|arXiv (Cornell University)|Dec 29, 2014

Black Holes and Theoretical Physics53 references9 citations

TL;DR

This study investigates thermoelectric and shear viscosities in a holographic anisotropic model dual to anisotropic $σ=4$ super-Yang-Mills theory with finite chemical potential, using perturbed linear axion fields to induce momentum relaxation. Key findings include a coherent/incoherent metal transition in ac conductivity, deviations from the Wiedemann-Franz law, violation of the Kovtun-Son-Starinets viscosity bound under prolate anisotropy, and non-equivalence between thermodynamic and dynamical instabilities as per the Gubser-Mitra conjecture.

ABSTRACT

We study thermoelectric conductivities and shear viscosities in a holographically anisotropic model, which is dual to a spatially anisotropic $\mathcal{N}=4$ super-Yang-Mills theory at finite chemical potential. Momentum relaxation is realized through perturbing the linear axion field. Ac conductivity exhibits a coherent/incoherent metal transition. Deviations from the Wiedemann-Franz law are also observed in our model. The longitudinal shear viscosity for prolate anisotropy violates the bound conjectured by Kovtun-Son-Starinets. We also find that thermodynamic and dynamical instabilities are not always equivalent by examining the Gubser-Mitra conjecture.

Motivation & Objective

• To explore thermoelectric and shear viscosity transport properties in anisotropic holographic models with finite chemical potential.
• To examine the impact of linear axion field perturbations on momentum relaxation and transport behavior.
• To test the validity of the Wiedemann-Franz law and the Kovtun-Son-Starinets viscosity bound in anisotropic settings.
• To investigate the relationship between thermodynamic and dynamical instabilities via the Gubser-Mitra conjecture.

Proposed method

• Employing gauge/gravity duality to model anisotropic $σ=4$ super-Yang-Mills theory with spatial anisotropy.
• Introducing momentum relaxation via perturbations of the linear axion field in the bulk gravitational background.
• Computing thermoelectric conductivities and shear viscosities using linear response theory in the holographic framework.
• Analyzing the ac conductivity to identify coherent/incoherent metal transitions.
• Evaluating the Wiedemann-Franz law deviation through the ratio of thermal to electrical conductivity.
• Applying the Gubser-Mitra criterion to compare thermodynamic and dynamical instability conditions.

Experimental results

Research questions

• RQ1 Does the ac conductivity in the anisotropic holographic model exhibit a coherent/incoherent metal transition?
• RQ2 To what extent do thermoelectric transport properties deviate from the Wiedemann-Franz law in this anisotropic system?
• RQ3 Is the Kovtun-Son-Starinets lower bound on shear viscosity violated under prolate anisotropy?
• RQ4 Are thermodynamic and dynamical instabilities always equivalent in this model, as per the Gubser-Mitra conjecture?

Key findings

• The ac conductivity exhibits a coherent/incoherent metal transition, indicating a change in the nature of charge transport due to anisotropy and momentum relaxation.
• Deviations from the Wiedemann-Franz law are observed, signaling non-Fermi liquid behavior in the anisotropic system.
• Longitudinal shear viscosity for prolate anisotropy violates the Kovtun-Son-Starinets viscosity bound, challenging the universality of the bound in anisotropic settings.
• Thermodynamic and dynamical instabilities are not equivalent in this model, indicating a breakdown of the Gubser-Mitra conjecture under certain anisotropic conditions.