Topological strings in d < 1

Abstract

We calculate correlation functions in minimal topological field theories. These twisted versions of N = 2 minimal models have recently been proposed to describe d < 1 matrix models, once coupled to topological gravity. In our calculation we make use of the Landau-Ginzburg formulation of the N = 2 models, and we find a direct relation between the Landau-Ginzburg superpotential and the KdV differential operator. Using this correspondence we show that the minimal topological models are in perfect agreement with the matrix models as solved in terms of the KdV hierarchy. This proves the equivalence at tree-level of topological and ordinary string thoery in d < 1.