D=4, N=1, Type IIA Orientifolds

We study D=4, N=1, type IIA orientifold with orbifold group $Z_N$ and $Z_N \times Z_M$. We calculate one-loop vacuum amplitudes for Klein bottle, cylinder and Mobius strip and extract the tadpole divergences. We find that the tadpole cancellation conditions thus obtained are satisfied by the $Z_4$, $Z_8$, $Z_8^{\mathrm{\prime }}$, $Z_{12}^{\mathrm{\prime }}$ orientifolds while there is no solution for $Z_3$, $Z_7$, $Z_6$, $Z_6^{\mathrm{\prime }}$, $Z_{12}$. The $Z_4\times Z_4$ 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 $Z_N$ orientifolds in four dimensions.