R-4 couplings in M- and type II theories on Calabi-Yau spaces

We discuss several implications of R-4 couplings in M-theory when compactified on Calabi-Yau (CY) manifolds. In particular, these couplings can be predicted by supersymmetry from the mixed gauge-gravitational Chem-Simons couplings in five dimensions and are related to the one-loop holomorphic anomaly in four-dimensional N = 2 theories, We find a new contribution to the Einstein term in five dimensions proportional to the Euler number of the internal CY threefold, which corresponds to a one-loop correction of the hypermultiplet geometry, This correction is reproduced by a direct computation in type II string theories, Finally, we discuss a universal non-perturbative correction to the type IIB hyper-metric. (C) 1997 Elsevier Science B.V.