On quantum corrected Kahler potentials in F-theory

We work out the exact in g(s) and perturbatively exact in alpha' result for the vector multiplet moduli Kahler potential in a specific N = 2 compactification of F-theory. The well-known alpha'(3) correction is absent, but there is a rich structure of corrections at all even orders in alpha'. Moreover, each of these orders independently displays an SL(2; Z) invariant set of corrections in the string coupling constant. This generalizes earlier findings to the case of a non-trivial elliptic fibration. Our results pave the way for the analysis of quantum corrections in the more complicated N = 1 context, and may have interesting implications for the study of moduli stabilization in string theory.