Chiral actions from phase space (quantum Hall) droplets

TL;DR

This paper develops a general framework for describing deformations of quantum Hall droplets on arbitrary manifolds, deriving their Hamiltonian and canonical structure, and capturing both edge states and quantum corrections.

Contribution

It introduces a transformation that decouples Casimirs, enabling a unified description of droplet deformations on any manifold, including nonlinear quantum effects.

Findings

Reproduces edge state chiral action in linearized theory

Derives Hamiltonian capturing 1/N quantum corrections

Provides a general method applicable to any manifold

Abstract

We derive the hamiltonian and canonical structure for arbitrary deformations of a phase space (quantum Hall) droplet on a general manifold of any dimension. The derivation is based on a transformation that decouples the Casimirs of the density Poisson structure. The linearized theory reproduces the edge state chiral action of the droplets, while the nonlinear hamiltonian captures 1/N quantum corrections.