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

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.