TYPE IIB ORIENTIFOLDS, F-THEORY, TYPE-I STRINGS ON ORBIFOLDS AND TYPEI-HETEROTIC DUALITY

We consider six- and four-dimensional N = 1 supersymmetric orientifold s of Type IIB compactified on orbifolds. We give the conditions under which the perturbative world-sheet orientifold approach is adequate, a nd list the four-dimensional N = 1 orientifolds (which are rather cons trained) that satisfy these conditions. We argue that in most cases or ientifolds contain non-perturbative sectors that are missing in the wo rld-sheet approach. These non-perturbative sectors can be thought of a s arising from D-branes wrapping various collapsed 2-cycles in the orb ifold, Using these observations, we explain certain ''puzzles'' in the literature on four-dimensional orientifolds, In particular, in some f our-dimensional orientifolds the ''naive'' tadpole cancellation condit ions have no solution. However, these tadpole cancellation conditions are derived using the world-sheet approach which we argue to be inadeq uate in these cases due to appearance of additional non-perturbative s ectors. The main tools in our analyses are the map between F-theory an d orientifold vacua and Type I-heterotic duality. Utilizing the consis tency conditions we have found in this paper, we discuss consistent fo ur-dimensional chiral N = 1 Type I vacua which are non-perturbative fr om the heterotic viewpoint. (C) 1998 Elsevier Science B.V.