Holographic DC conductivities from the open string metric

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.