Classification of the N=2, Z(2) x Z(2)-symmetric type II orbifolds and their type II asymmetric duals

Using free world-sheet fermions, we construct and classify all the N = 2, Z (2) x Z(2) four-dimensional orbifolds of the type IIA/B strings for which t he orbifold projections oct symmetrically on the left- and right-movers. We study the deformations of these models out of the fermionic point, derivin g the partition functions at a generic point in the moduli of the internal torus T-6 = T-2 x T-2 x T-2. We investigate some of their perturbative and non-perturbative dualities and construct new dual pairs of type IIA/type II asymmetric orbifolds, which are related nonperturbatively and allow us to gain insight into some of the non-perturbative properties of the type IIA/B strings in four dimensions. In particular, we consider some of the (non-)p erturbative gravitational corrections. (C) 1999 Elsevier Science B.V. All r ights reserved.