Abstract
Models of random surfaces defined by means of integrals over quaternion-real self-dual random matrices are solved exactly in a double-scaling limit. Coupled nonlinear ordinary differential equations are obtained for the specific heat, which takes the form {ital r}+{ital w}{prime}, where {ital r} is the specific heat of the corresponding Hermitian-matrix model, and {ital w} satisfies a nonlinear differential equation depending on {ital r}. It is shown that the {ital k}=2 theory, which may describe a new phase of two-dimensional quantum gravity, is unitary. An alternative method of solution, based on a set of symplectically orthogonal polynomials, is indicated.
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