From M-theory higher curvature terms to α' corrections in F-theory

Abstract: We perform a Kaluza-Klein reduction of eleven-dimensional supergravity on a Calabi-Yau fourfold including terms quartic and cubic in the Riemann curvature and determine the induced corrections to the three-dimensional N=2 effective action. We focus on the effective Einstein-Hilbert term and the kinetic terms for vectors. Dualizing the vectors into scalars, we derive the resulting Kahler potential and complex coordinates. The classical expressions for the Kahler coordinates are non-trivially modified, while the functional form of the Kahler potential is shown to be uncorrected. For elliptically fibered Calabi-Yau fourfolds the corrections can be uplifted to a four-dimensional F-theory compactification. We argue that also the four-dimensional N=1 Kahler coordinates receive non-trivial corrections. We find a simple expression for the induced corrections for different Abelian and non-Abelian seven-brane configurations by scanning over many Calabi-Yau fourfolds with resolved singularities. The interpretation of this expression leads us to conjecture that the higher-curvature corrections correspond to \alpha'^2 corrections that arise from open strings at the self-intersection of seven-branes.