Chiral Rings and Physical States in c < 1 String Theory

Abstract We show how the double cohomology of the string and Felder BRST charges naturally leads to the ring structure of c x p ⋍ y p+1 for the (p + 1, p) model. We also study the states corresponding to the edges of the conformal grid whose inclusion is crucial for the closure of the ring. We introduce candidate operators that correspond to the observables of the matrix models. Their existence is motivated by the relation of one of the screening operators of the minimal model to the zero momentum dilaton.