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

2003/07/31 by Dimitra Karabali, V. P. Nair · 5 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #cond-mat.mes-hall #hep-th

paper · pdf · doi:10.1016/j.nuclphysb.2003.11.020

published as Nucl.Phys. B679 (2004) 427-446 · 22 pages, LaTeX, discussion on nature of edge states for S^4 added to section 5, final version to appear in Nucl. Phys. B

arxiv created 2003/11/19 · openalex publication_date 2003/12/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

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 \bf 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 S⁴ with an SU(2) background magnetic field, using the fact that \bf CP³ is an S² bundle over S⁴.

Citations

• Non-commutative algebra of functions of 4-dimensional quantum Hall droplet

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