Kac-Moody theories for colored phase space (quantum Hall) droplets

TL;DR

This paper develops a theoretical framework for describing deformations of higher-dimensional quantum Hall droplets with spin or color, using Kac-Moody algebra and gauge fields on phase space.

Contribution

It introduces a higher-dimensional generalization of gauged Kac-Moody algebra for quantum Hall droplets with spin or color, including gauge fields via Kaluza-Klein construction.

Findings

Derives canonical structure and Hamiltonian for droplet deformations

Reproduces edge state chiral Wess-Zumino-Witten action at leading order

Provides a nonlinear higher-dimensional algebraic description

Abstract

We derive the canonical structure and hamiltonian for arbitrary deformations of a higher-dimensional (quantum Hall) droplet of fermions with spin or color on a general phase space manifold. Gauge fields are introduced via a Kaluza-Klein construction on the phase space. The emerging theory is a nonlinear higher-dimensional generalization of the gauged Kac-Moody algebra. To leading order in h-bar this reproduces the edge state chiral Wess-Zumino-Witten action of the droplet.