The role of the spin connection in quantum Hall effect: A perspective from geometric quantization

Abstract

The topological terms of the bulk effective action for the integer quantum Hall effect, capturing the dynamics of gauge and gravitational fluctuations, reveal a curiosity, namely, the Abelian potential for the magnetic field appears in a particular combination with the Abelian spin connection. This seems to hold for quantum Hall effect on complex projective spaces of arbitrary dimensions. An interpretation of this in terms of the algebra of symplectic transformations is given. This can also be viewed in terms of the metaplectic correction in geometric quantization.

arXiv comment15 pages

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Cited by in corpus (4)

• Fractional Quantum Hall Effect for Extended Objects: from Skyrmionic Membranes to Dyonic Strings
• Noncommutative Geometry and Deformation Quantization in the Quantum Hall Fluids with Inhomogeneous Magnetic Fields
• Entanglement for Quantum Hall states and a Generalized Chern-Simons Form
• Matter-gravity coupling for fuzzy geometry and the Landau-Hall problem