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; 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 [Formula: see text] duality of the scalar field theory at the edge.