On four-derivative terms in IIB Calabi-Yau orientifold reductions

We perform a Kaluza-Klein reduction of IIB supergravity including purely gravitational $\alpha '^3$-corrections on a Calabi-Yau threefold, and perform the orientifold projection accounting for the presence of $O3/O7$-planes. We consider infinitesimal K\"{a}hler deformations of the Calabi-Yau background and derive the complete set of four-derivative couplings quadratic in these fluctuations coupled to gravity. In particular, we find four-derivative couplings of the K\"{a}hler moduli fields in the four-dimensional effective supergravity theory, which are referred to as friction couplings in the context of inflation.