Gribov horizon, contact terms and Čech- De Rham cohomology in 2D topological gravity

Abstract

We point out that averages of equivariant observables of 2D topological gravity are not globally defined forms on moduli space, when one uses the functional measure corresponding to the formulation of the theory as a 2D superconformal model. This is shown to be a consequence of the existence of the Gribov horizon {\it and} of the dependence of the observables on derivatives of the super-ghost field. By requiring the absence of global BRS anomalies, it is nevertheless possible to associate global forms to correlators of observables by resorting to the Čech-De Rham notion of form cohomology. To this end, we derive and solve the ``descent'' of local Ward identities which characterize the functional measure. We obtain in this way an explicit expression for the Čech-De Rham cocycles corresponding to arbitrary correlators of observables. This provides the way to compute and understand contact terms in string theory from first principles.

Uses harvmac, 33 pages (big) or 20 pages (little)

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• The Coupling of Chern-Simons Theory to Topological Gravity
• The topological structure of supergravity: an application to supersymmetric localization
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• Modular Invariant Regularization of String Determinants and the Serre GAGA Principle
• Symmetries and observables in topological gravity
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