Non-perturbative effect of a modified action in matrix models

A modified matrix model action, which may provide the well-defined two dimensional pure gravity theory, proposed by Das, Dhar, Sengupta and Wadia is analyzed non-perturbatively. The perturbative solution in genus expansion is also obtained. It is shown that the specific heat satisfies Painleve equation in the double scaling limit. Thus the modified action is found to be in the same universality class as ordinary matrix models.