Orientifold in Conifold and Quantum Deformation

TL;DR

This paper explores the orientifold operation in the conifold background, deriving O3 planes from O4 planes via T-duality, and discusses their implications for duality cascades and quantum deformations in the gauge theory.

Contribution

It introduces a new description of orientifolds in the conifold, analyzes their effects on the dual gauge theory, and discusses the limitations of supergravity in distinguishing orientifold types.

Findings

O3^+ and O3^- are located at the tip of the cone with no net untwisted RR charge.

Two fractional branes are required for conformal invariance in the orientifolded conifold.

Gravity solutions are indistinguishable between different orientifold types, matching Klebanov-Tseytlin solutions.

Abstract

We describe orientifold operation defining O3 plane in the conifold background 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 need two `fractional' branes for the conformal invariance in orientifolded conifold. We argue that the gravity solution is the same as Klebanov and Tsyetlin since SUGRA cannot distinguish the orientifolds and D branes in this case. We describe the duality cascade as well as the quantum deformation of the 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.