The supersymmetric effective action of the heterotic string in ten dimensions

Abstract

We construct the supersymmetric completion of quartic R + R 4-actions in the ten-dimensional effective action of the heterotic string. Two invariants, of which the bosonic parts are known from one-loop string amplitude calculations, are obtained. One of these invariants can be generalized to an R + F 2 + F 4-invariant for supersymmetric Yang-Mills theory coupled to supergravity. Supersymmetry requires the presence of B ∧ R ∧ R ∧ R ∧ R-terms, ( B ∧ F ∧ F ∧ F ∧ F for Yang-Mills) which correspond to counterterms in the Green-Schwarz anomaly cancellation. Within the context of our calculation the ζ(3) R 4-term from the tree-level string effective action does not allow supersymmetrization.