Remarks on the Hall Conductivity in Chiral Superconductors: Weak vs. Strong Coupling Approach

We discuss the calculations of the ac Hall conductivity for superconductors with the time reversal symmetry breaking states. In the weak coupling theories these states show vanishing Hall response in one band models, even though one expects otherwise on symmetry grounds. On the other hand, the strong coupling approach based on the anti-de Sitter-conformal field theory correspondence leads to the non-vanishing Hall conductivity. We discuss the possible reasons of the discrepancy. The weak coupling many orbital theory leading to the Hall conductivity with correct temperature dependence is also briefly presented.