On quantum corrected Kähler potentials in F-theory

We work out the exact in g s and perturbatively exact in α′ result for the vector multiplet moduli Kähler potential in a specific N=2 compactification of F-theory. The well-known α ′3 correction is absent, but there is a rich structure of corrections at all even orders in α ′ . 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.