Open string field theory of strong interactions in two dimensions

Abstract

This is a review of some old work by the author from a new perspective: as a string field theory of strong interactions in two dimensional space-time that is equivalent to two dimensional QCD. The open string field, in light cone co-ordinates, is just a function of the endpoints. The key idea is that this field must satisfy a quadratic constraint, analogous to the constraint satisfied by the field of the non-linear sigma model. All the interactions arise as a result of this constraint: the manifold of solutions of the constraints is an infinite dimensional Grassmannian. The classical string field theory is equivalent to the large N limit of 2DQCD; by quantizing it we recover 2DQCD for finite N. The linear approximation to our theory is the original large N limit of 2DQCD constructed by 't Hooft. Baryons arise as topological solitons.