Chiral Anomaly and Effective Field Theory for the Quantum Hall Liquid with Edges

Details Chiral Anomaly and Effective Field Theory for the Quantum Hall Liquid with Edges Chiral Anomaly and Effective Field Theory for the Quantum Hall Liquid with Edges

1995-07-26

arxiv.org/abs/hep-th/9507138v3

Phys.Lett. B376 (1996) 142-147

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, LaTex, figures not included, references are added

Scientific paper

10.1016/0370-2693(96)00274-2

Under general assumptions, we present a low-energy effective action for the quantum Hall state when edges exist. It is shown that the chiral edge current is necessary to make the effective action to be gauge invariant. However the chiral edge current is irrelevant to the Hall current. The exactly quantized value of $\sigma_{xy}$ is observed only when the Hall current does not flow at the edge region. Our effective theory is applicable to the quantum Hall liquid on a surface with non-trivial topology and physical meanings of the topology are discussed.

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