The Geometry of Quantum Hall Effect: An Effective Action for all Dimensions

Abstract

We present a general formula for the topological part of the effective action for quantum Hall systems in higher dimensions, including fluctuations of the gauge field and metric around background fields of a specified topological class. The result is based on a procedure of integrating up from the Dolbeault index density which applies for the degeneracies of Landau levels, combined with some input from the standard descent procedure for anomalies. Features of the topological action in (2+1), (4+1), (6+1) dimensions, including the contribution due to gravitational anomalies, are discussed in some detail.

34 pages; references added, minor corrections and clarifications; version to appear in PRD

References in corpus (10)

• Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect
• Density-curvature response and gravitational anomaly
• Topological central charge from Berry curvature: gravitational anomalies in trial wavefunctions for topological phases
• Quantum Hall Effect in Higher Dimensions, Matrix Models and Fuzzy Geometry
• Geometric adiabatic transport in quantum Hall states
• Quantum Hall effect and Quillen metric
• Higher Dimensional Quantum Hall Effect as A-Class Topological Insulator
• Multipole Expansion in the Quantum Hall Effect
• Bosonization of the lowest Landau level in arbitrary dimensions: edge and bulk dynamics
• The Matrix Chern-Simons One-form as a Universal Chern-Simons Theory

Cited by in corpus (15)

• Topological Electromagnetic Responses of Bosonic Quantum Hall, Topological Insulator, and Chiral Semi-Metal phases in All Dimensions
• $SO(4)$ Landau Models and Matrix Geometry
• Geometric quench in the fractional quantum Hall effect: exact solution in quantum Hall matrix models and comparison with bimetric theory
• Ergodic Edge Modes in the 4D Quantum Hall Effect
• Hall viscosity and geometric response in the Chern-Simons matrix model of the Laughlin states
• Fractional Quantum Hall Effect for Extended Objects: from Skyrmionic Membranes to Dyonic Strings
• The role of the spin connection in quantum Hall effect: A perspective from geometric quantization
• Hall Viscosity in the Non-Abelian Quantum Hall Matrix Model
• ADHM and the 4d Quantum Hall Effect
• Entanglement entropy for integer quantum Hall effect in two and higher dimensions
• $SO(5)$ Landau Model and 4D Quantum Hall Effect in The $SO(4)$ Monopole Background
• Geometry and large N limits in Laughlin states
• Entanglement for Quantum Hall states and a Generalized Chern-Simons Form
• Matter-gravity coupling for fuzzy geometry and the Landau-Hall problem
• Fractional Quantum Hall States on CP2 Space