Exactly Solvable Supercritical String Theories?

Abstract

By analytically continuing the string equations of the subcritical Type 0A (2, 4|m|) minimal string theories, we reveal a whole new family of differential and integro-differential equations associated with the naively supercritical (2, -4|m|) theories. We uncover an elegant structure, associated with the negative KdV hierarchy, that in principle yields the exact partition functions of the models for all values of the string coupling. Furthermore, the physics associated with the new equations displays many of the salient features associated with the original subcritical models, plus other new phenomena that are not present in those cases. One such phenomenon may have an interpretation as a tachyon condensation process by which the theories can change their dimensionalities.