Prepotential, mirror map and F-theory on K3

Abstract

We compute certain one-loop corrections to F4 couplings of the heterotic string compactified on T2, and show that they can be characterized by holomorphic prepotentials G. We then discuss how some of these couplings can be obtained in F-theory, or more precisely from 7-brane geometry in type IIB language. We in particular study theories with E8 × E8 and SO(8)4 gauge symmetry, on certain one-dimensional sub-spaces of the moduli space that correspond to constant IIB coupling. For these theories, the relevant geometry can be mapped to Riemann surfaces. Physically, the computations amount to non-trivial tests of the basic F-theory - heterotic duality in eight dimensions. Mathematically, they mean to associate holomorphic 5-point couplings of the form ∂t5G ~ σ gℓℓ5 qℓ 1-qℓ to K3 surfaces. This can be seen as a novel manifestation of the mirror map, acting here between open and closed string sectors. © 1999 International Press.