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

Abstract

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.

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

References in corpus (5)

• Conformal Symmetry and Universal Properties of Quantum Hall States
• One-Dimensional Fermions as Two-Dimensional Droplets Via Chern-Simons Theory
• W_{\infty} Gauge Transformations and the Electromagnetic Interactions of Electrons in the Lowest Landau Level
• Duality and the Fractional Quantum Hall Effect
• Charged and Neutral Vortex Excitations in a Mean Field Theory for the Fractional Quantum Hall Effect

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• Bulk Versus Edge in the Quantum Hall Effect
• Magnetic Response in Quantized Spin Hall Phase of Correlated Electrons
• Topological bulk states and their currents
• Edge modes in the fractional quantum Hall effect without extra edge fermions
• Gauge anomaly cancellation in chiral gauge theories
• Harada-Tsutsui Gauge Recovery Procedure: From Abelian Gauge Anomalies to the Stueckelberg Mechanism
• Boundary degrees of freedom in fractional quantum Hall effect: Excitations on common boundary of two samples