Orientifold in Conifold and Quantum Deformation

We describe orientifold operation defining O3 plane in the conifold background by deriving it from that of O4 plane in the T-dual Type IIA brane construction. We find that the O3 plane can exist only at the tip of the cone. We discuss how to reconcile this fact with the deformed or resolved conifold where there is no fixed point of the orientifold operation. We also show that we need two `fractional' branes for the conformal invariance so that the theory should have gauge group $SO(N+2) \times Sp(N)$. We give several explanations for this. We describe the duality cascade and chiral symmetry breaking as well as the quantum deformation of the moduli space of the field theory in the presence of the conifold.