Conductivity in the anisotropic background

TL;DR

This paper uses gauge/gravity duality to analyze electrical conductivity in anisotropic backgrounds, revealing conditions for metallic and strange metal behaviors through different gauge field fluctuations.

Contribution

It provides a classification of conductivities in anisotropic holographic models, highlighting how dilaton coupling influences the frequency dependence of conductivity.

Findings

AC conductivity can have negative frequency exponents in certain parameters.

Conductivity exponents are always positive when gauge fields are uncoupled from the dilaton.

The model captures strange metal-like behavior in specific anisotropic backgrounds.

Abstract

By using the gauge/gravity duality, we investigate the dual field theories of the anisotropic backgrounds, which are exact solutions of Einstein-Maxwell-dilaton theory with a Liouville potential. When we turn on the bulk gauge field fluctuation $A_x$ with a non-trivial dilaton coupling, the AC conductivity of this dual field theory is proportional to the frequency with an exponent depending on parameters of the anisotropic background. In some parameter regions, we find that this conductivity can have the negative exponent like the strange metal. In addition, we also investigate another U(1) gauge field fluctuation, which is not coupled with a dilaton field. We classify all possible conductivities of this system and find that the exponent of the conductivity is always positive.