ar X iv : h ep - t h / 99 08 01 7 v 2 2 O ct 1 99 9 HUE - 99 / 1 July 1999 D = 4 , N = 1 , Type IIA Orientifolds

We study D = 4, N = 1, type IIA orientifold with orbifold group ZN and ZN × ZM . We calculate one-loop vacuum amplitudes for Klein bottle, cylinder and Möbius strip and extract the tadpole divergences. We find that the tadpole cancellation conditions thus obtained are satisfied by the Z4, Z8, Z ′ 8, Z ′ 12 orientifolds while there is no solution for Z3, Z7, Z6, Z ′ 6, Z12. The Z4 × Z4 type IIA orientifold is also constructed by introducing four different configurations of 6-branes. We argue about perturbative versus non-perturbative orientifold vacua under T-duality between the type IIA and the type IIB ZN orientifolds in four dimensions.