The effective action for edge states in higher dimensional quantum Hall systems

Abstract

We show that the effective action for the edge excitations of a quantum Hall droplet of fermions in higher dimensions is generically given by a chiral bosonic action. We explicitly analyze the quantum Hall effect on complex projective spaces ${\mathbf{CP}}^k$ with a U(1) background magnetic field. The edge excitations are described by abelian bosonic fields on $S^{2k-1}$ with only one spatial direction along the boundary of the droplet relevant for the dynamics. Our analysis also leads to an action for edge excitations for the case of the Zhang-Hu four dimensional quantum Hall effect defined on $S^4$ with an SU(2) background magnetic field, using the fact that ${\mathbf{CP}}^3$ is an $S^2$ bundle over $S^4$.

22 pages, LaTeX, discussion on nature of edge states for S^4 added to section 5, final version to appear in Nucl. Phys. B

References in corpus (10)

• A Four Dimensional Generalization of the Quantum Hall Effect
• Quantum Hall Effect in Higher Dimensions
• Fermions in the Lowest Landau Level: Bosonization, $W_{\infty }$ Algebra, Droplets, Chiral Boson
• Noncommutative Gauge Theory on Fuzzy Four-Sphere and Matrix Model
• Effective field theory description of the higher dimensional quantum Hall liquid
• One-Dimensional Fermions as Two-Dimensional Droplets Via Chern-Simons Theory
• Higher-Dimensional Quantum Hall Effect in String Theory
• Non-commutative geometry of 4-dimensional quantum Hall droplet
• Gravitational fields on a noncommutative space
• Collective Variables of Fermions and Bosonization

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