Electromagnetic interactions of higher dimensional quantum Hall droplets

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

15 pages, LaTeX, typos corrected, minor additions

References in corpus (5)

• Dissipationless Quantum Spin Current at Room Temperature
• Experimental observation of the spin-Hall effect in a two dimensional spin-orbit coupled semiconductor system
• Chiral actions from phase space (quantum Hall) droplets
• Fuzzy spaces, the M(atrix) model and the quantum Hall effect
• Kac-Moody theories for colored phase space (quantum Hall) droplets

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• D-string fluid in conifold: I. Topological gauge model
• D-string fluid in conifold: II. Matrix model for D-droplets on S^{3} and S^{2}
• Landau-Hall States and Berezin-Toeplitz Quantization of Matrix Algebras
• The Matrix Chern-Simons One-form as a Universal Chern-Simons Theory
• Thermofield dynamics and Gravity
• The role of the spin connection in quantum Hall effect: A perspective from geometric quantization
• Entanglement entropy for integer quantum Hall effect in two and higher dimensions
• Noncommutative Fluids
• Noncommutative Geometry and Deformation Quantization in the Quantum Hall Fluids with Inhomogeneous Magnetic Fields
• CP(n) supersymmetric mechanics in U(n) background gauge fields
• Entanglement for Quantum Hall states and a Generalized Chern-Simons Form
• Symmetries of N=4 supersymmetric CP(n) mechanics
• Matter-gravity coupling for fuzzy geometry and the Landau-Hall problem
• Symplectic Fluctuations for Electromagnetic Excitations of Hall Droplets
• Fermion liquids as quantum Hall liquids in phase space: A unified approach for anomalies and responses
• Electromagnetic Excitations of A_n Quantum Hall Droplets
• Electromagnetic Excitations of Hall Systems on Four Dimensional Space