String-induced gravity and ghost-freedom

Abstract

The order α′k^4 four-point graviton amplitudes calculated from the bosonic, heterotic and supersymmetric strings are shown to be derivable from effective gravitational actions in which multiples of the Gauss-Bonnet quadratic curvature contribution are added to the Einstein action. However, it is also explicitly shown that on Einstein shell, the terms proportional to R_(μν)^2 and R^2 do not contribute to the amplitudes. This result implies that the effective graviton propagator is always non-ghost, a conclusion which remains valid for all higher orders. The calculations provide explicit diagrammatic verification of the field redefinition mechanism and of the fact that the exchange plus contact terms generated by the effective action yield the (expanded) string amplitudes.