NONPERTURBATIVE SOLUTION OF MATRIX MODELS MODIFIED BY TRACE-SQUARED TERMS

We present a non-perturbative solution of large N matrix models modified by terms of the form g(Tr Phi(4))(2), which add microscopic wormholes to the random surface geometry. For g < g(t) the sum over surfaces is in the same universality class as the g = 0 theory, and the string susceptibility exponent is reproduced by the conventional Liouville interaction similar to e(alpha+phi). For g = g(t) we find a different universality class, and the string susceptibility exponent agrees for any genus with Liouville theory where the interaction term is dressed by the other branch, e(alpha-phi). This allows us to define a double-scaling limit of the g = g(t) theory. We also consider matrix models modified by terms of the form gO(2), where O is a scaling operator. A fine-tuning of g produces a change in this operator's gravitational dimension which is, again, in accord with the change in the branch of the Liouville dressing.