Ramond-Ramond corrections to type II supergravity at order $\alpha'^3$

Abstract

Recently, it has been shown that the NS-NS corrections to the type II supergravity given by Gross and Sloan are invariant under the linear T-duality. In this paper, we study the invariance of this action under sequence of S-duality and linear T-duality to find the R-R corrections to the supergravity at order $\alpha'^3$, up to field redefinition.