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

Abstract

We investigate the non-perturbative equivalence of some heterotic/type II dual pairs with N = 2 supersymmetry. The perturbative heterotic scalar manifolds are respectively SU(1, 1)/ U(1) × SO(2,2+ N V )/ SO(2) × SO(2+ N V ) and SO(4,4+ N H )/ SO(4) × SO(4+ N H ) for moduli in the vector multiplets and hypermultiplets. The models under consideration correspond, on the type II side, to self-mirror Calabi-Yau threefolds with Hodge numbers h 1,1 = N V + 3 = h 2,1 = N H + 3, which are K3 fibrations. We consider three classes of dual pairs, with N V = N H = 8, 4 and 2. The models with h 1,1 = 7 and 5 provide new constructions, while the h 1,1 = 11, already studied in the literature, is reconsidered here. Perturbative R 2-like corrections are computed on the heterotic side by using a universal operator whose amplitude has no singularities in the ( T, U) space, and can therefore be compared with the type II side result. We point out several properties connecting K3 fibrations and spontaneous breaking of the N = 4 supersymmetry to N = 2. As a consequence of the reduced S- and T- duality symmetries, the instanton numbers in these three classes are restricted to integers, which are multiples of 2, 2 and 4, for N V = 8, 4 and 2, respectively.