A Possible IIB Superstring Matrix Model with Euler Characteristic and a Double Scaling Limit

We show that a recently proposed Yang-Mills matrix model with an auxiliary field, which is a candidate for a non-perturbative description of type IIB superstrings, captures the Euler characteristic of moduli space of Riemann surfaces. This happens at the saddle point for the Yang-Mills field. It turns out that the large-n limit in this matrix model corresponds to a double scaling limit in the Penner model. E-mail: [email protected] E-mail: [email protected] The conjecture by Banks, Fischler, Shenker, and Susskind [1] that M theory is an n = ∞ matrix model, has induced a large activity towards a non-perturbative formulation of type IIB superstrings by matrix models. It has been proposed by Ishibashi, Kawai, Kitazawa, and Tsuchiya (IKKT) [2] that the large-n reduced model of ten-dimensional super Yang-Mills theory can be considered as such a formulation, provided the matrix size, n, is considered as a dynamical variable to be summed from n = 0 to n = ∞ in the partition function. It was recently proposed [3] that this sum over all n, which is somewhat foreign to the n = ∞ philosophy, should be replaced by an auxiliary matrix field Y i j , and the large-n limit taken, thereby avoiding introducing small-n matrices. The partition function is then given by [3]