Computations on B-model geometric transitions

TL;DR

This paper investigates geometric transitions on Calabi-Yau manifolds using the B-model, demonstrating the equivalence of a nontrivial example and highlighting limitations of the conifold transition.

Contribution

It provides a detailed mathematical analysis of a nontrivial geometric transition in the B-model, advancing understanding beyond simple conifold cases.

Findings

Confirmed the expected equivalence in a nontrivial example

Showed the conifold transition is too simple for meaningful results

Worked out the mathematics of a complex geometric transition

Abstract

We study geometric transitions on Calabi- Yau manifolds from the perspective of the $B$ model. Looking toward physically motivated predictions, it is shown that the traditional conifold transition is too simple a case to yield meaningful results. The mathematics of a nontrivial example (of Aganagic and Vafa) is worked out carefully, and the expected equivalence is demonstrated.