Edge States for quantum Hall droplets in higher dimensions and a generalized WZW model

Abstract

We consider quantum Hall droplets on complex projective spaces with a combination of abelian and nonabelian background magnetic fields. Carrying out an analysis similar to what was done for abelian backgrounds, we show that the effective action for the edge excitations is given by a chiral, gauged Wess-Zumino-Witten (WZW) theory generalized to higher dimensions.

27 pages, LaTeX, references added, discussion enlarged

References in corpus (17)

• A Four Dimensional Generalization of the Quantum Hall Effect
• Quantum Hall Effect in Higher Dimensions
• Fermions in the Lowest Landau Level: Bosonization, $W_{\infty }$ Algebra, Droplets, Chiral Boson
• The Eight Dimensional Quantum Hall Effect and the Octonions
• Four-Dimensional Avatars of Two-Dimensional RCFT
• Noncommutative Gauge Theory on Fuzzy Four-Sphere and Matrix Model
• Effective field theory description of the higher dimensional quantum Hall liquid
• Conformal Symmetry and Universal Properties of Quantum Hall States
• The effective action for edge states in higher dimensional quantum Hall systems
• One-Dimensional Fermions as Two-Dimensional Droplets Via Chern-Simons Theory
• Higher-Dimensional Quantum Hall Effect in String Theory
• Quantum Hall effect on $S^3$, edge states and fuzzy $S^3/{\mathbf{Z}}_2$
• Non-commutative geometry of 4-dimensional quantum Hall droplet
• Gravitational fields on a noncommutative space
• Higher-dimensional WZW Model on Kähler Manifold and Toroidal Lie Algebra
• Collective Variables of Fermions and Bosonization
• Exact microscopic wave function for a topological quantum membrane

Cited by in corpus (49)

• Bergman Kernel from Path Integral
• Chiral actions from phase space (quantum Hall) droplets
• A matrix model for a quantum hall droplet with manifest particle-hole symmetry
• Fuzzy spaces, the M(atrix) model and the quantum Hall effect
• Quantum Hall Effect on Higher Dimensional Spaces
• Random normal matrices, Bergman kernel and projective embeddings
• Kac-Moody theories for colored phase space (quantum Hall) droplets
• Electromagnetic interactions of higher dimensional quantum Hall droplets
• Quantum Oscillator on $\DC P^n$ in a constant magnetic field
• The Geometry of Quantum Hall Effect: An Effective Action for all Dimensions
• The Chern-Simons One-form and Gravity on a Fuzzy Space
• Construction of fuzzy S^4
• Bosonization of the lowest Landau level in arbitrary dimensions: edge and bulk dynamics
• Effective Wess-Zumino-Witten Action for Edge States of Quantum Hall Systems on Bergman Ball
• Landau-Hall States and Berezin-Toeplitz Quantization of Matrix Algebras
• Quantum Hall Effect on the Flag Manifold F_2
• The Matrix Chern-Simons One-form as a Universal Chern-Simons Theory
• Ergodic Edge Modes in the 4D Quantum Hall Effect
• Bosonization in higher dimensions via noncommutative field theory
• Quantum Hall Effect on Odd Spheres
• Thermofield dynamics and Gravity
• A Quantum Ring in a Nanosphere
• The role of the spin connection in quantum Hall effect: A perspective from geometric quantization
• Fractional Quantum Hall Effect for Extended Objects: from Skyrmionic Membranes to Dyonic Strings
• ADHM and the 4d Quantum Hall Effect
• Entanglement entropy for integer quantum Hall effect in two and higher dimensions
• Noncommutative Fluids
• The fermion density operator in the droplet bosonization picture
• Quantum Hall Effect on the Grassmannians ${\mathbf{Gr}}_2({\mathbb{C}}^N)$
• Analytic non-Abelian gravitating solitons in the Einstein-Yang-Mills-Higgs theory and transitions between them
• Symplectic Deformations, Non Commutative Scalar Fields and Fractional Quantum Hall Effect
• On the Gauge-invariant Functional Measure for Gauge Fields on CP^2
• Entanglement for Quantum Hall states and a Generalized Chern-Simons Form
• Gauge and Scalar Fields on ${\mathbb{CP}}^2$: A Gauge-invariant Analysis II. The measure for gauge fields and a 4d WZW theory
• Fermi Surface Bosonization for Non-Fermi Liquids
• Exact operator Hamiltonians and interactions in the droplet bosonization method
• Gauge and Scalar Fields on ${\mathbb{CP}}^2$: A Gauge-invariant Analysis I. The effective action from chiral scalars
• Matter-gravity coupling for fuzzy geometry and the Landau-Hall problem
• Matrix oscillator and Laughlin Hall states
• Symplectic Fluctuations for Electromagnetic Excitations of Hall Droplets
• 5d-4d Correspondence in Twisted M-theory on a Conifold
• Noncommutative Wess-Zumino-Witten actions and their Seiberg-Witten invariance
• Holomorphicity, Vortex Attachment, Gauge Invariance and the Fractional Quantum Hall Effect
• Noncommutative scalar fields from symplectic deformation
• Electromagnetic Excitations of Hall Systems on Four Dimensional Space
• Electromagnetic Excitations of A_n Quantum Hall Droplets
• A gauge-invariant measure for gauge fields on ${\mathbb{CP}}^2$
• A note on the Hamiltonian structure of transgression forms
• Critical theory of Pomeranchuk transitions via high-dimensional bosonization