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

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.