On the origin of duality in the quantum Hall system

TL;DR

This paper explores the origin of duality in quantum Hall systems, emphasizing the role of modular symmetry in explaining observed dualities in current-voltage behavior.

Contribution

It clarifies the distinction between particle-vortex and charge-flux dualities and advocates for a modular symmetry-based explanation consistent with experimental data.

Findings

Modular symmetry explains the observed duality in quantum Hall systems.

The complexified conductivity transforms holomorphically under the symmetry.

Experimental data supports the modular symmetry origin of duality.

Abstract

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.