Non-perturbative orientifold transitions at the conifold

TL;DR

This work analyzes the non-perturbative fate of the conifold singularity after orientifolding in Type IIA, focusing on O6-planes and D6-branes on the deformed conifold. By lifting to M-theory and employing Vafa-type superpotentials, the authors map the quantum moduli space across various D6-brane charges, revealing smooth and phase transitions governed by the total RR charge, including non-BPS bolts driving transitions and a clarified ${ m Z}_2$ D0-brane charge. They construct new ${ m G}_2$ holonomy geometries (${ f B}_7$, ${f A}_7$, ${ f D}_7$), analyze their symmetries, and demonstrate how the orientifold charge changes by the vanishing-cycle class during conifold transitions. The results yield a detailed, charge-sensitive picture of how semi-classical limits (deformed vs resolved conifolds with various fluxes) connect or disconnect, with exact branching for $N=1$ via a Type IIB mirror. Overall, the paper advances understanding of non-perturbative connectivity in ${ m N}=1$ Calabi–Yau moduli spaces under orientifolds and provides a framework applicable to broader geometric transitions in string theory.

Abstract

After orientifold projection, the conifold singularity in hypermultiplet moduli space of Calabi-Yau compactifications cannot be avoided by geometric deformations. We study the non-perturbative fate of this singularity in a local model involving O6-planes and D6-branes wrapping the deformed conifold in Type IIA string theory. We classify possible A-type orientifolds of the deformed conifold and find that they cannot all be continued to the small resolution. When passing through the singularity on the deformed side, the O-plane charge generally jumps by the class of the vanishing cycle. To decide which classical configurations are dynamically connected, we construct the quantum moduli space by lifting the orientifold to M-theory as well as by looking at the superpotential. We find a rich pattern of smooth and phase transitions depending on the total sixbrane charge. Non-BPS states from branes wrapped on non-supersymmetric bolts are responsible for a phase transition. We also clarify the nature of a Z_2 valued D0-brane charge in the 6-brane background. Along the way, we obtain a new metric of G_2 holonomy corresponding to an O6-plane on the three sphere of the deformed conifold.

Figures (16)

• Figure 1: Is a $\mu$-transition possible? When complexified with the RR field, the moduli space can be smooth or it can have a real codimension two singularity.
• Figure 2: Representations of the 5 orientifolds of the deformed conifold in Type IIA theory. The orientifold loci are the fixed points of the anti-holomorphic involution. The cases (1) and (3) break supersymmetry when D6-branes are wrapped on $S^3$ and they are related by taking $\mu \rightarrow -\mu$.
• Figure 3: Parameter space of smooth initial data for ${\mathbb B}_7$. The metric has sensible asymptotics only when the initial data is on one of the three half lines $C_{1,2,3}$ bounding the regions (I), (II), (III).
• Figure 4: Parameter space of smooth initial data for the space ${\mathbb A}_7/{\mathbb Z}_2,{\mathbb A}_7$ with fixed scale. The metric behaves nicely when the initial data is chosen from one of the curves $C_{1,2,3}$ separating the three regions (I), (II), (III). The special point $P$ corresponds to $(A_1,A_2,A_3,B_1,B_2,B_3)=(1,0,1,1,.9171,1)$.
• Figure 5: The quantum moduli space for the cases $N>3$. Here $\mu$ and $t$ are the sizes of deformation and resolution.