SYMMETRIES AND MASS SPLITTINGS IN QCD2 COUPLED TO ADJOINT FERMIONS

Two-dimensional QCD coupled to fermions in the adjoint representation of the gauge group SU(N), a useful toy model of QCD strings, is supersymmetric for a certain ratio of quark mass and gauge coupling constant. Here we study the theory in the vicinity of the supersymmetric point; in particular we exhibit the algebraic structure of the model and show that the mass splittings as one moves away from the supersymmetric point obey a universal relation of the form M(i)2(B) - M(i)2(F) = M(i)deltam + O(deltam3). We discuss the connection of this relation to string and quark model expectations and verify it numerically for large N. At least for low lying states the O(deltam3) corrections are extremely small. We also discuss a natural generalization of QCD2 with an infinite number of couplings, which preserves SUSY. This leads to a Landau-Ginzburg description of the theory, and may be useful for defining a scaling limit in which smooth worldsheets appear.