On the origin of duality in the quantum Hall system

We discuss the possible origin of the duality observed in the quantum Hall current–voltage characteristics. We clarify the difference between “particle–vortex” (complex modular) duality, which acts on the full transport tensor, and “charge–flux” (“real”) duality, which acts directly on the filling factor. Comparison with experiment strongly favors the form of duality which descends from the modular symmetry group acting holomorphically on the complexified conductivity.