Thermoelectric conductivities, shear viscosity, and stability in an anisotropic linear axion model

TL;DR

This paper investigates thermoelectric conductivities, shear viscosities, and stability in an anisotropic holographic model, revealing phenomena like metal transitions, violations of viscosity bounds, and differences between thermodynamic and dynamical stability.

Contribution

It introduces a holographic anisotropic model with momentum relaxation, analyzing transport properties and stability, and uncovers violations of known viscosity bounds and stability conjectures.

Findings

AC conductivity shows a metal transition

Shear viscosity violates Kovtun-Son-Starinets bound

Thermodynamic and dynamical instabilities are not always aligned

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.