Chern-Simons Duality and the Quantum Hall Effect

Abstract

In previous work on the quantum Hall effect on an annulus, we used $O(d,d;{\bf Z})$ duality transformations on the action describing edge excitations to generate the Haldane hierarchy of Hall conductivities. Here we generate the corresponding hierarchy of ``bulk actions'' which are associated with Chern-Simons (CS) theories, the connection between the bulk and edge arising from the requirement of anomaly cancellation. We also find a duality transformation for the CS theory exactly analogous to the $R\rightarrow \frac{1}{R}$ duality of the scalar field theory at the edge.