Bosonization of the lowest Landau level in arbitrary dimensions: edge and bulk dynamics

Abstract

We discuss the bosonization of nonrelativistic fermions interacting with non-Abelian gauge fields in the lowest Landau level in the framework of higher dimensional quantum Hall effect. The bosonic action is a one-dimensional matrix action, which can also be written as a noncommutative field theory, invariant under $W_N$ transformations. The requirement that the usual gauge transformation should be realized as a $W_N$ transformation provides an analog of a Seiberg-Witten map, which allows us to express the action purely in terms of bosonic fields. The semiclassical limit of this, describing the gauge interactions of a higher dimensional, non-Abelian quantum Hall droplet, produces a bulk Chern-Simons type term whose anomaly is exactly cancelled by a boundary term given in terms of a gauged Wess-Zumino-Witten action.

arXiv comment29 pages ; typos corrected, two references added

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Cited by in corpus (15)

• The Geometry of Quantum Hall Effect: An Effective Action for all Dimensions
• Landau-Hall States and Berezin-Toeplitz Quantization of Matrix Algebras
• Thermofield dynamics and Gravity
• The role of the spin connection in quantum Hall effect: A perspective from geometric quantization
• Entanglement entropy for integer quantum Hall effect in two and higher dimensions
• Noncommutative Fluids
• CP(n) supersymmetric mechanics in U(n) background gauge fields
• 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
• Exact operator Hamiltonians and interactions in the droplet bosonization method
• Matter-gravity coupling for fuzzy geometry and the Landau-Hall problem
• Symplectic Fluctuations for Electromagnetic Excitations of Hall Droplets
• Noncommutative Wess-Zumino-Witten actions and their Seiberg-Witten invariance
• Electromagnetic Excitations of A_n Quantum Hall Droplets
• Electromagnetic Excitations of Hall Systems on Four Dimensional Space