Reduction of affine two-loop WZNW model, the Toda system coupled to the matter and topological confinement

TL;DR

This paper derives an affine Toda model coupled to matter from a two-loop WZNW model, showing it exhibits linear confinement similar to QCD in two dimensions, and connects it to sine-Gordon theory.

Contribution

It introduces a new integrable field theory derived from a classical reduction of the affine WZNW model, demonstrating confinement and QCD-like features.

Findings

The model exhibits linear quark-antiquark confinement at large distances.

Bosonization reveals a connection to sine-Gordon and free scalar fields.

The effective theory models low-energy QCD with one flavor and two colors.

Abstract

The conformal affine Toda model coupled to the matter field (CATM) is obtained through a classical reduction of the $sl(2)^{(1)}$ affine two-loop WZNW model. After spontaneously broken the conformal symmetry by means of BRST analysis, we end up with an effective theory, the so called affine Toda model coupled to the matter (ATM). Further, using a bosonization technique we recover from this theory the sine-Gordon model plus a free massless scalar field. The ATM model is considered as a QCD-motivated integrable field theory, since it describes various features in the baryonic sector of the low-energy effective Lagrangian of QCD in two dimensions with one flavor and two colors. Imposing the equivalence of the Noether and topological currrents as a constraint, it is shown that the intercharge ``quark''- ``anti-quark'' static potential reveals a linear confinement behavior for large intercharge separation.