Higher-Genus Contributions to an Induced Supergravity Action

Abstract

The higher-genus contributions to a supergravity action induced by the evaluation of the superstring path integral are considered. Three extra terms are found in the BRST transformation that would arise in the supergravity action. The supersymmetric BRST contour integral over the ideal boundary of an in.nite-genus surface is found to be vanishing if the harmonic measure is zero. The e.ect of a conformal transformation is demonstrated to be consistent with the vanishing of the BRST superspace contour integral. Since the commutator of BRST and conformal Since the BRST symmetry and conformal transformations transofrmations is proportional to the .rst current in four-dimensional gravity, and the vacuum is invariant under both transformations, conditions on the worldsheet .elds result from the dynamics in the embedding space. A connection between conformal models on the two-dimensional worldsheet and the quantum action of the gravitational theory in four dimensions is established through the ghost sector. The number of degrees of freedom in the gravity theory must be reduced to achieve this result. The introduction of new variables related to the embedding of two-dimensional surfaces in three-geometries and then fourmanifolds is then required to satisfy the condition of quantum consistency characteristic of conformal .eld theories.