On the universality class of the conifold

TL;DR

This paper investigates the nature of conifold singularities with discrete torsion, concluding that no additional localized discrete degrees of freedom exist and that obstructions are topological rather than local.

Contribution

It demonstrates that D-brane probe theories near conifold singularities with discrete torsion are equivalent to ordinary conifolds, clarifying the topological nature of singularity resolutions.

Findings

No extra discrete degrees of freedom at conifold singularities.

Obstructions to resolution are topological, not local.

Evidence that singularity properties can be inferred from topological data.

Abstract

The possibility of having discrete degrees of freedom at singularities associated to `conifolds with discrete torsion' is studied. We find that the field theory of D-brane probes near these singularities is identical to ordinary conifolds, so that there are no additional discrete degrees of freedom located at the singularity. We shed light on how the obstructions to resolving the singularity are global topological issues rather that local obstrucions at the singularity itself. We also analyze the geometric transitions and duality cascades when one has fractional branes at the singularity and compute the moduli space of an arbitrary number of probes in the geometry. We provide some evidence for a conjecture that there are no discrete degrees of freedom localized at any Calabi-Yau singularity that can not be guessed from topological data away from the singularity.