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

TL;DR

The paper probes transport in strongly interacting 2+1D CFTs using AdS/CFT by modeling the system with a dyonic AdS$_4$ black hole. It derives the complex electrical conductivities, and from them the thermoelectric and thermal coefficients, uncovering a relativistic cyclotron resonance and revealing how bulk $SL(2,Z)$ duality governs the transport. Analytic results in the hydrodynamic regime and numerical solutions at general frequency, magnetic field, and charge density show consistency with magnetohydrodynamics and predict duality-driven pole/zero structures. The work connects holographic transport to experimental probes such as the Nernst effect near quantum critical points and points to extensions involving momentum, disorder, and other holographic backgrounds. Overall, it provides a unified holographic framework for Ohm's law at strong coupling with a clear role for duality and cyclotron dynamics.

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.

Figures (4)

• Figure 1: A density plot of $|\sigma_+|$ as a function of complex $w$. White areas are large in magnitude and correspond to poles while dark areas are zeroes of $\sigma_+$: a) $h=0$ and $q=1$, b) $h=q=1/\sqrt{2}$, c) $h=1$ and $q=0$.
• Figure 2: The dashed blue line is the $\hbox{Im}(\sigma_+)$ while the solid red line is the $\hbox{Re}(\sigma_+)$ as a function of $w$: a) $h=q=1/\sqrt{2}$, b) $h=1$ and $q=0$.
• Figure 3: The location of the pole closest to the origin as a function of $h$ for $q=-0.1$. The data points are numerically determined locations of the pole. The curves show the limiting hydrodynamic behavior. Plots (c) and (d) are closeups of the hydrodynamic region in plots (a) and (b).
• Figure 4: The location of the pole closest to the origin as a function of $-q$ for $h=0.1$. The data points are numerically determined locations of the pole. The curves show the limiting hydrodynamic behavior.