Current Algebra in Three Dimensions

TL;DR

This paper explores a three-dimensional analogue of the Wess--Zumino--Witten model, deriving a current algebra similar to Kac--Moody algebra, relevant for understanding Goldstone bosons in 3D QCD.

Contribution

It introduces a three-dimensional generalization of the current algebra associated with the Wess--Zumino--Witten model, connecting topological terms to Chern--Simons forms.

Findings

Derived the three-dimensional current algebra using canonical methods.

Established the relation between the topological term and Chern--Simons form.

Extended the Kac--Moody algebra to three dimensions.

Abstract

We study a three dimensional analogue of the Wess--Zumino--Witten model, which describes the Goldstone bosons of three dimensional Quantum Chromodynamics. The topologically non--trivial term of the action can also be viewed as a nonlinear realization of Chern--Simons form. We obtain the current algebra of this model by canonical methods. This is a three dimensional generalization of the Kac--Moody algebra.