Ohm's Law at strong coupling: S duality and the cyclotron resonance

TL;DR

This paper explores the transport properties of strongly coupled 2+1D conformal field theories with holographic duals, revealing how duality influences conductivities and identifying a cyclotron resonance feature.

Contribution

It provides analytic formulas for electrical conductivity at low frequencies and demonstrates the role of S duality in transport phenomena within holographic models.

Findings

Electrical conductivity exhibits a cyclotron pole.

Thermal conductivity and thermoelectric coefficient are determined by electrical conductivity.

Bulk electromagnetic duality acts on transport coefficients.

Abstract

We calculate the electrical and thermal conductivities and the thermoelectric coefficient of a class of strongly interacting 2+1 dimensional conformal field theories with anti-de Sitter space duals. We obtain these transport coefficients as a function of charge density, background magnetic field, temperature and frequency. We show that the thermal conductivity and thermoelectric coefficient are determined by the electrical conductivity alone. At small frequency, in the hydrodynamic limit, we are able to provide a number of analytic formulae for the electrical conductivity. A dominant feature of the conductivity is the presence of a cyclotron pole. We show how bulk electromagnetic duality acts on the transport coefficients.