CHERN-SIMONS DUALITY AND THE QUANTUM HALL-EFFECT

In previous work on the quantum Hall effect on an annulus, we used O(d , d; Z) duality transformations on the action describing edge excitati ons to generate the Haldane hierarchy of Hall conductivities. Here we generate the corresponding hierarchy of ''bulk actions'' which are ass ociated with Chern-Simons (CS) theories, the connection between the bu lk and edge arising from the requirement of anomaly cancellation. We a lso find a duality transformation for the CS theory exactly analogous to the R --> 1/R duality of the scalar field theory at the edge.