# Hall conductivity from dyonic black holes

## TL;DR

This paper uses holographic duality to compute the Hall conductivity of a strongly interacting 2+1D conformal field theory in a magnetic field, finding it equals the ratio of charge density to magnetic field.

## Contribution

It provides a holographic calculation of Hall conductivity in a strongly coupled 2+1D CFT with magnetic field, confirming the expected ratio from field theory.

## Key findings

- Hall conductivity equals charge density divided by magnetic field
- Derived from perturbations of dyonic AdS black holes
- Supports holographic approach to condensed matter phenomena

## 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.