Hall conductivity from dyonic black holes

TL;DR

This paper uses the AdS/CFT correspondence to study Hall transport in strongly interacting 2+1D CFTs under a background magnetic field by modeling the boundary theory with a dyonic AdS4 black hole. It derives zero-momentum hydrodynamic response functions and, via the Kubo formula, shows the Hall conductivity satisfies $\sigma_{xy} = \rho/B$, consistent with Lorentz invariance, while diagonal conductivities vanish. In addition to the Hall response, the authors compute current-momentum and momentum-momentum correlators, clarifying the hydrodynamic regime and the limits of validity, and discuss implications for magnetohydrodynamics in strongly coupled CFTs. The work demonstrates how holographic methods can yield analytic insights into transport phenomena in 2+1D CFTs with external fields and paves the way for further explorations of magnetic-field effects in holographic magnetohydrodynamics.

Abstract

A class of strongly interacting 2+1 dimensional conformal field theories in a transverse magnetic field can be studied using the AdS/CFT duality. We compute zero momentum hydrodynamic response functions of maximally supersymmetric 2+1 dimensional SU(N) Yang-Mills theory at the conformal fixed point, in the large N limit. With background magnetic field B and electric charge density rho, the Hall conductivity is found to be rho/B. The result, anticipated on kinematic grounds in field theory, is obtained from perturbations of a four dimensional AdS black hole with both electric and magnetic charges.