Schwinger-Dyson equations in reduced, quenched, chiral models

It is shown that Schwinger-Dyson equations for the infinite volume U(N) chiral model and the reduced chiral model, quenched according to Parisi's prescription, agree to leading order in N for all values of the coupling and in any number of dimension d. The conditions under which these equations can determine a theory uniquely are discussed. It is concluded that the two models are equivalent for d<=dsub(c)=2, but not necessarily for d>dsub(c). (orig.)