The Ramond Ramond sector of string theory beyond leading order

Present knowledge of higher-derivative terms in string effective actions is, with a few exceptions, restricted to the NS NS sector, a situation which prevents the development of a variety of interesting applications for which the RR terms are relevant. We here provide the formalism as well as efficient techniques to determine the latter directly from string-amplitude calculations. As an illustration of these methods, we compute the dependence of the type-IIB action on the 3- and 5-form RR field strengths at four-point, genus-one, order-(α')³ level. We explicitly verify that our results are in accord with the {\rm SL}(2,{\bb Z}) S-duality invariance of type-IIB string theory. Extensions of our method to other bosonic terms in the type-II effective actions are also discussed.