Conductivities from attractors

TL;DR

This paper calculates electrical and thermal conductivities of dual field theories using black hole solutions in Einstein-Maxwell-dilaton theories, revealing specific scaling behaviors at zero temperature.

Contribution

It introduces a method combining near-horizon data with known formulas to compute conductivities without explicit background solutions.

Findings

Thermoelectric conductivity scales as N^{3/2} at zero temperature.

Heat conductivity remains finite and scales as N^{3/2} as T approaches zero.

Method applies to models with unknown explicit background geometries.

Abstract

In the context of applications of the AdS/CFT correspondence to condensed matter physics, we compute conductivities for field theory duals of dyonic planar black holes in 3+1-dimensional Einstein-Maxwell-dilaton theories at zero temperature. We combine the near-horizon data obtained via Sen's entropy function formalism with known expressions for conductivities. In this way we express the conductivities in terms of the extremal black hole charges. We apply our approach to three different examples for dilaton theories for which the background geometry is not known explicitly. For a constant scalar potential, the thermoelectric conductivity explicitly scales as $\alpha_{xy}\sim N^{3/2}$, as expected. For the same model, our approach yields a finite result for the heat conductivity $\kappa/T \propto N^{3/2}$ even for $T \rightarrow 0$.