Orientifold in conifold and quantum deformation

We describe orientifold operation defining O3 plane in the conifold backgro und by deriving it from that of O4 plane in the Type IIA brane construction by T-duality. We find that both O3(+) and O3(-) are at the tip of the cone so that there is no net untwisted RR charge. RG analysis shows that we nee d two 'fractional' branes for the conformal invariance in orientifolded con ifold. We argue that the gravity solution is the same as Klebanov and Tseyt lin since SUGRA cannot distinguish the orientifolds and D branes in this ca se. We describe the duality cascade as well as the quantum deformation of t he moduli space of the field theory in the presence of the orientifold. The finitely resolved conifold does not allow the orientifold, while deformed conifold leaves us an unresolved issue on supersymmetry. (C) 2001 Elsevier Science B.V. All rights reserved.