Exact amplitudes in four-dimensional non-critical string theories

The large N expansion of N = 2 supersymmetric Yang-Mills theory with gauge group SU(N) has recently been shown to break down at singularities on the moduli space. We conjecture that by taking N --> infinity and approaching the singularities in a correlated way, all the observables of the theory have a finite universal limit yielding amplitudes in string theories dual to field theories describing the light degrees of freedom. We explicitly calculate the amplitudes corresponding to the Seiberg-Witten period integrals for an A(n-1) series of multicritical points as well as for other critical points exhibiting a scaling reminiscent of the c = 1 matrix model. Our results extend the matrix model approach to non-critical strings in less than one dimension to non-critical strings in four dimensions. (C) 2001 Published by Elsevier Science B.V.