Exactly solvable self-dual strings

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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 r+w’, where r is the specific heat of the corresponding Hermitian-matrix model, and w satisfies a nonlinear differential equation depending on r. It is shown that the 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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