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 ρ, the Hall conductivity is found to be ρ/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.
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Hartnoll et al. (2007) studied this question.
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