Matrix Models as Superstrings

Abstract

We propose an extension of Marinari and Parisi's supersymmetric one dimensional strings. This model is expected to describe superstring in less than one dimension. The target space of these string theories is a finite lattice with supersymmetry. The supersymmetry guarantees that the free energy of the matrix model, i.e., the vacuum amplitude of the corresponding string theory, vanishes in any order of the perturbation. When the number of matrices is odd, the supersymmetry breaks down in general. On the other hand, the supersymmetry never breaks down when the number is even. We analyze the correlation functions in one matrix model which will be equivalent to zero dimensional superstring theory in the large N limit. This model is closely related to the bosonic two dimensional gravity coupled with c = -2 conformal matter (-2 dimensional string theory). When Nicolai's mapping is degenerate, there exists a critical point and the continuum limit can be defined to all orders in the genus expansion. We consider the string susceptibility and compare it with those of the known two dimensional gravity theories. Furthermore we analyze two matrix model and we show that there exists a multi critical point.