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

The non-perturbative equivalence of four-dimensional N = 2 superstrings with three vector multiplets and four hypermultiplets is analysed. These models are obtained through freely acting orbifold compactifications from the heterotic, the symmetric and the asymmetric type II strings. The heterotic scalar 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 hypermultiplets. The type II symmetric duals correspond to a self-mirror Calabi-Yau threefold compactification with Hodge numbers h^1,1 = h^2,1 = 3, while the type II asymmetric construction corresponds to a spontaneous breaking of the 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 that there is a weak/strong coupling S-duality relation between the heterotic and the asymmetric type IIA ground state with 47πS_Het = - (4πS_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-)perturbative R² and F² corrections and determine the prepotential.