Title: Aspects of higher dimensional quantum Hall effect: Effective actions, entanglement entropy

Abstract: I will present the formulation of higher dimensional QHE on complex projective spaces, with both abelian (electromagnetic) and nonabelian background fields and derive the effective actions describing the edge/bulk dynamics and the responses to changes in the external gauge and gravitational fields (related to the Hall conductivity, Hall viscosity, etc). I will also discuss the calculation of the entanglement entropy for such systems. In the case of the LLL, a semiclassical analysis shows that the entanglement entropy is proportional to the phase-space area of the entangling surface with a universal overall constant, same for any dimension as well as abelian or nonabelian background magnetic fields.