GRIBOV PROBLEM, CONTACT TERMS AND CECH-DE RHAM COHOMOLOGY IN 2D TOPOLOGICAL GRAVITY

We point out that averages of equivariant observables of 2D topologica l gravity are not globally defined forms on moduli space, when one use s the functional measure corresponding to the formulation of the theor y as a 2D superconformal model. This is shown to be a consequence of t he existence of the Gribov horizon and of the dependence of the observ ables on derivatives of the super-ghost field, By requiring the absenc e of global BRS anomalies, it is nevertheless possible to associate gl obal forms to correlators of observables by resorting to the Cech-De R ham cohomology, To this end, we derive and solve the ''descent'' of lo cal Ward identities which characterize the functional measure, We obta in in this way an explicit expression for the Cech-De Rham cocycles co rresponding to arbitrary correlators of observables. This provides the way to compute and understand contact terms in string theory from fir st principles.