Abstract
Using a W N -gauge theory to describe electromagnetic interactions of spinless fermions in the lowest Landau level, where the W N transformations are nonlinear realizations of U ( 1 ) gauge transformations, we construct the effective action describing electromagnetic interactions of a higher-dimensional quantum Hall droplet. We also discuss how this is related to the Abelian Seiberg–Witten map. Explicit calculations are presented for the quantum Hall effect on CP k with U ( 1 ) background magnetic field. The bulk action is a Kähler–Chern–Simons term whose anomaly is canceled by a boundary contribution so that gauge invariance is explicitly satisfied.
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