Holographic DC conductivities from the open string metric

TL;DR

This paper introduces a new geometric approach using the open string metric to compute DC conductivities in holographic models, simplifying calculations and providing deeper insights into transport phenomena like quantum Hall effects and strange metals.

Contribution

It proposes a novel method employing the open string metric for calculating nonlinear DC conductivities, offering geometric interpretation and technical advantages over previous methods.

Findings

The OSM method simplifies conductivity calculations.

Application to quantum Hall and strange metal models shows parameter effects.

Comparison of backgrounds reveals temperature scaling changes.

Abstract

We study the DC conductivities of various holographic models using the open string metric (OSM), which is an effective metric geometrizing density and electromagnetic field effect. We propose a new way to compute the nonlinear conductivity using OSM. As far as the final conductivity formula is concerned, it is equivalent to the Karch-O'Bannon's real-action method. However, it yields a geometrical insight and technical simplifications. Especially, a real-action condition is interpreted as a regular geometry condition of OSM. As applications of the OSM method, we study several holographic models on the quantum Hall effect and strange metal. By comparing a Lifshitz background and the Light-Cone AdS, we show how an extra parameter can change the temperature scaling behavior of conductivity. Finally we discuss how OSM can be used to study other transport coefficients, such as diffusion constant, and effective temperature induced by the effective world volume horizon.