Orientifolds and type II dual pairs

In this paper we present a symmetry of a toroidally compactified type II string theory. This symmetry has the interpretation that it interchanges the left- and the right-moving world sheet coordinates and reverses the orientations of some of the spatial coordinates. We also identify another discrete symmetry of the type II theory which is related to the above one by a nontrivial U-duality element of string theory. This symmetry, however, has a trivial action on the world sheer coordinates and corresponds to an improper T-duality rotation. We then construct examples of type II dual pairs in four dimensions by modding out the known type II dual pairs by the above symmetries. We show the explicit matching of the spectrum and supersymmetries in these examples.