Non-perturbative triality in heterotic and type II N=2 strings

The non-perturbative equivalence of four-dimensional N = 2 superstrings wit h three vector multiplets and four hypermultiplets is analysed. These model s are obtained through freely acting orbifold compactifcations from the het erotic, the symmetric and the asymmetric type II strings. The heterotic sca lar manifolds are (SU(1, 1)/U(1))(3) for the S, T, U moduli sitting in the vector multiplets and SO(4, 4)/(SO(4) x SO(4)) for those in the hypermultip lets. The type II symmetric duals correspond to a self-mirror Calabi-Yau th reefold compactification with Wedge numbers h(1.1) = h(2.1) = 3, while the type II asymmetric construction corresponds to a spontaneous breaking of th e N = (4, 4) supersymmetry to N = (2, 0). Both have already been considered in the literature. The heterotic construction instead is new and we show t hat there is a weak/strong coupling S-duality relation between the heteroti c and the asymmetric type IIA ground state with 4 pi S-Het = -(4 pi S-As)(- 1); we also show that there is a partial restoration of N = 8 supersymmetry in the heterotic strong-coupling regime. We compute the full (non-)perturb ative R-2 and F-2 corrections and determine the prepotential. (C) 1999 Else vier Science B.V. All rights reserved.