Non-perturbative gravitational corrections in a class of N = 2 string duals

We investigate the non-perturbative equivalence of some heterotic/type II d ual pairs with N = 2 supersymmetry. The perturbative heterotic scalar manif olds are respectively SU(1, 1)/U(1) x SO(2, 2 + N-V)/SO(2) x SO(2 + N-V) an d SO(4, 4 + N-H)/SO(4) x SO(4 + N-H) for moduli in the vector multiplets an d hypermultiplets. The models under consideration correspond, on the type I I side, to self-mirror Calabi-Yau threefolds with Hedge numbers h(1,1) = N- V + 3 = h(2,1) = N-H + 3, which are K3 fibrations. We consider three classe s of dual pairs, with N-V = N-H = 8, 4 and 2. The models with h(1,1) = 7 an d 5 provide new constructions, while the h(1,1) = 11, already studied in th e literature, is reconsidered here. Perturbative R-2-like corrections are c omputed on the heterotic side by using a universal operator whose amplitude has no singularities in the (T, U) space, and can therefore be compared wi th the type II side result. We point out several properties connecting K3 f ibrations and spontaneous breaking of the N = 4 supersymmetry to N = 2. As a consequence of the reduced S- and T- duality symmetries, the instanton nu mbers in these three classes are restricted to integers, which are multiple s of 2, 2 and 4, for N-V = 8, 4 and 2, respectively. (C) 1999 Elsevier Scie nce B.V.