Electromagnetic interactions of higher dimensional quantum Hall droplets

Details Electromagnetic interactions of higher dimensional quantum Hall droplets Electromagnetic interactions of higher dimensional quantum Hall droplets

2005-07-02

arxiv.org/abs/hep-th/0507027v2

Nucl.Phys. B726 (2005) 407-420

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, LaTeX, typos corrected, minor additions

Scientific paper

10.1016/j.nuclphysb.2005.08.025

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 ${\bf CP}^k$ with U(1) background magnetic field. The bulk action is a K\"ahler-Chern-Simons term whose anomaly is cancelled by a boundary contribution so that gauge invariance is explicitly satisfied.

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