Conifolds and geometric transitions

Abstract

Conifold geometries have recieved much attention in string theory and string-inspired cosmology recently, in particular the Klebanov-Strassler background that is known as the ''warped throat.'' This paper provides a pedagogical explanation for the singularity resolution in this geometry and emphasizes its connection to geometric transitions. The first part focuses on the gauge theory dual to the Klebanov-Strassler background, including the T-dual intersecting branes description. Then, a connection to the Gopakumar-Vafa conjecture for open-closed string duality is presented and a series of papers verifying this model on the supergravity level is summarized. An appendix provides extensive background material about conifold geometries. Special attention is given to their complex structures and the supersymmetry conditions on the background flux in constructions with fractional D3-branes on the singular (Klebanov-Tseytlin) and resolved (Pando Zayas-Tseytlin) conifolds are reevaluated. In agreement with earlier results, it is shown that only the singular solution allows a supersymmetric flux. However, the importance of using the correct complex structure to reach this conclusion is emphasized.