Aspects of Higher Dimensional Quantum Hall Effect: Effective Actions and Entanglement Entropy

Explore the formulation of higher dimensional quantum Hall effect (QHE) on complex projective spaces in this comprehensive lecture. Delve into both abelian (electromagnetic) and nonabelian background fields, and examine the derivation of effective actions describing edge/bulk dynamics and responses to changes in external gauge and gravitational fields. Investigate the calculation of entanglement entropy for these systems, with a focus on the Lowest Landau Level (LLL). Discover how a semiclassical analysis reveals that entanglement entropy is proportional to the phase-space area of the entangling surface, featuring a universal overall constant across dimensions and background magnetic field types. Learn from Dimitra Karabali's presentation, which covers topics such as Hall conductivity, Hall viscosity, and the universal nature of entanglement entropy in higher dimensional QHE systems.