The Ramond-Ramond sector of string theory beyond leading order

TL;DR

This paper develops a formalism and techniques to compute higher-derivative Ramond-Ramond terms in string effective actions directly from string amplitudes, exemplified by calculations in type-IIB theory that confirm S-duality invariance.

Contribution

It introduces a new method to determine RR sector higher-derivative terms from string amplitudes, extending the understanding of string effective actions beyond the NS-NS sector.

Findings

Computed RR field dependence at four-point, genus-one, order-(alpha')^3 level.

Verified SL(2,Z) S-duality invariance in type-IIB string theory.

Discussed extensions to other terms in type-II effective actions.

Abstract

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 three- and five-form RR field strengths at four-point, genus-one, order-(alpha')^3 level. We explicitly verify that our results are in accord with the SL(2,Z) S-duality invariance of type-IIB string theory. Extensions of our method to other bosonic terms in the type-II effective actions are discussed as well.