String Field Theory of Two Dimensional QCD: A Realization of W-infinity Algebra

TL;DR

This paper formulates two-dimensional QCD using gauge-invariant bilocal operators that satisfy a W-infinity algebra, deriving an action and analyzing meson spectra and baryonic configurations within this algebraic framework.

Contribution

It introduces a string field theory formulation of 2D QCD based on W-infinity algebra, deriving the action, constraints, and analyzing meson and baryon structures.

Findings

Derivation of an action for bilocal string fields in 2D QCD.

Identification of meson spectra as representations of W-infinity algebra.

Discussion of baryons as stringy solitons characterized by W-infinity algebra.

Abstract

We consider the formulation of two dimensional QCD in terms of gauge invariant bilocal operators (string field) which satisfy a $W_\infty$ algebra. In analogy with our work on the $c=1$ string field theory we derive an action and associated constraints for the bilocal field using the method of coadjoint orbits. The $1/N$ perturbation theory around a classical solution that corresponds to the filled Dirac sea leads to the 'tHooft equation for meson fluctuations. It is shown that the spectrum of mesons, which are the higher string modes, transform as a representation of the wedge subalgebra $W_{\infty+} \otimes W_{\infty-}$. We briefly discuss the baryon as a stringy solitonic configuration and its characterization in terms of $W_\infty$ algebra.