Conformal Edge Currents in Chern-Simons Theories

TL;DR

This paper presents a canonical quantization approach for Chern-Simons theories that naturally produces edge states and boundary symmetries without gauge fixing, connecting to Kac-Moody and Sugawara structures.

Contribution

It introduces a gauge-independent canonical method for quantizing Chern-Simons actions, elucidating boundary states and diffeomorphism generators in a clear, elementary framework.

Findings

Derivation of edge states carrying Kac-Moody algebra representations

Canonical expressions for boundary diffeomorphism generators

Connection to Sugawara construction in Chern-Simons theories

Abstract

We develop elementary canonical methods for the quantization of abelian and nonabelian Chern-Simons actions using well known ideas in gauge theories and quantum gravity. Our approach does not involve choice of gauge or clever manipulations of functional integrals. When the spatial slice is a disc, it yields Witten's edge states carrying a representation of the Kac-Moody algebra. The canonical expression for the generators of diffeomorphisms on the boundary of the disc are also found, and it is established that they are the Chern-Simons version of the Sugawara construction. This paper is a prelude to our future publications on edge states, sources, vertex operators, and their spin and statistics in 3D and 4D topological field theories.