$W_\infty$ Algebra and Geometric Formulation of QCD$_2$

TL;DR

This paper reviews the gauge-invariant formulation of two-dimensional QCD, highlighting its phase space structure as a coset related to the $W_$ algebra and discussing the stringy nature of baryons as solitons.

Contribution

It introduces a geometric formulation of 2D QCD using $W_$ algebra and describes the phase space and soliton coordinates in this framework.

Findings

Phase space is the coset $W_/W_{+} imes W_{-}$.

Meson fields are local coordinates of the coset.

Baryons are described as solitons with stringy collective coordinates.

Abstract

We review the gauge invariant formulation of 2-dim. QCD. We show that the non-linear gauge invariant phase space is the coset $W_\infty/W_{+\infty}\times W_{-\infty}$ ,which is specified by the $N=\infty$ master-field of this model. The meson fields correspond to the local coordinates of the coset. We comment on the stringy collective coordinates of the solitons (baryons) in this model.