String field theory of two dimensional QCD: a realization of W_∞ algebra

Abstract

We consider the formulation of two dimensional QCD in terms of gauge invariant bilocal operators (string field) which satisfy a W_∞ 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 't Hooft equation for meson fluctuations. It is shown that the spectrum of mesons, which are higher string modes, transform as a representation of the wedge subalgebra W_∞⁺ ⊗ W_∞^-. We briefly discuss the baryon as a stringy solitonic configuration and its characterization in terms of W_∞ algebra.