F-theory vacua and α′-corrections

In this work we analyze F-theory and Type IIB orientifold compactifications to study alpha '-corrections to the four-dimensional, N = 1 effective actions. In particular, we obtain corrections to the Kahlermoduli space metric and its complex structure for generic dimension originating from eight-derivative corrections to eleven-dimensional supergravity. We propose a completion of the G(2)R(3) and ( backward difference G)R-2(2)-sector in eleven-dimensions relevant in Calabi-Yau fourfold reductions. We suggest that the three-dimensional, N = 2 Kahler coordinates may be expressed as topological integrals depending on the first, second, and third Chern-forms of the divisors of the internal Calabi-Yau fourfold. The divisor integral Ansatz for the Kahler potential and Kahler coordinates may be lifted to four-dimensional, N= 1 F-theory vacua. We identify a novel correction to the Kahler potential and coordinates at order alpha '(2), which is leading compared to other known corrections in the literature. At weak string coupling the correction arises from the intersection of D7-branes and O7-planes with base divisors and the volume of self-intersection curves of divisors in the base. In the presence of the conjectured novel alpha '-correction resulting from the divisor interpretation the no-scale structure may be broken. Furthermore, we propose a model independent scenario to achieve non-supersymmetric AdS vacua for Calabi-Yau orientifold backgrounds with negative Euler-characteristic.