Conifolds and Geometric Transitions

TL;DR

This paper explains conifold geometries and their role in string theory, focusing on singularity resolution, geometric transitions, and their dual gauge theories, with detailed background and analysis of supersymmetry conditions.

Contribution

It provides a pedagogical overview of conifold singularities, their resolution, and the connection to geometric transitions and dual gauge theories, including detailed flux and complex structure analysis.

Findings

Singular conifold solutions allow supersymmetric flux with correct complex structure.

Geometric transitions relate conifold singularities to smooth geometries.

Verification of open/closed string duality models at the supergravity level.

Abstract

Conifold geometries have recieved a lot of attention in string theory and string-inspired cosmology recently, in particular the Klebanov-Strassler background that is known as the "warped throat". It is our intention in this article to give a pedagogical explanation for the singularity resolution in this geometry and emphasise its connection to geometric transitions. The first part focuses on the gauge theory dual to the Klebanov-Strassler background, which we also explain from a T-dual intersecting branes scenario. We then make the connection to the Gopakumar-Vafa conjecture for open/closed string duality and summarise a series of papers verifying this model on the supergravity level. An appendix provides extensive background material about conifold geometries. We pay special attention to their complex structures and re-evaluate the supersymmetry conditions on the background flux in constructions with fractional D3-branes on the singular (Klebanov-Tseytlin) and resolved (Pando Zayas-Tseytlin) conifolds. We agree with earlier results that only the singular solution allows a supersymmetric flux, but point out the importance of using the correct complex structure to reach this conclusion.