Chiral splitting and world-sheet gravitinos in higher-derivative string amplitudes

We report on progress made in the construction of higher-derivative superinvariants for type-II theories in ten dimensions. The string amplitude calculations required for this analysis exhibit interesting features which have received little attention in the literature so far. We discuss two examples from a forthcoming publication: the construction of the (H-NS)R-2(3) terms and the femionic completion of the epsilonepsilon R-4 terms. We show that a correct answer requires very careful treatment of the chiral splitting theorem, implies unexpected new relations between fermionic correlators, and most interestingly, necessitates the use of world-sheet gravitino zero modes in the string vertex operators. In addition we compare the relation of our results to the predictions of the linear scalar superfield of the type-IIB theory.