Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-07-29
Nucl.Phys. B679 (2004) 427-446
Physics
High Energy Physics
High Energy Physics - Theory
22 pages, LaTeX, discussion on nature of edge states for S^4 added to section 5, final version to appear in Nucl. Phys. B
Scientific paper
10.1016/j.nuclphysb.2003.11.020
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 $S^4$ with an SU(2) background magnetic field, using the fact that ${\bf CP}^3$ is an $S^2$ bundle over $S^4$.
Karabali Dimitra
Nair V. P.
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