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 compexified conductivity.