Topological String Partition Function on Generalised Conifolds

TL;DR

This paper demonstrates that the topological string partition function on a generalised conifold with multiple crepant resolutions can be computed using a simpler singularity model, simplifying calculations in string theory.

Contribution

It establishes an equivalence between the partition function on a generalised conifold and a compound du Val singularity, providing a new computational approach.

Findings

Partition function on $C_{m,n}$ can be computed via $A_{m+n-1} imes C$ singularity.

Number of crepant resolutions for $C_{m,n}$ is ${m+n rack m}$.

Simplifies calculations of topological string partition functions.

Abstract

We show that the partition function on a generalised conifold $C_{m,n}$ with ${m+n \choose m}$ crepant resolutions can be equivalently computed on the compound du Val singularity $A_{m+n-1}\times \mathbb C$ with a unique crepant resolution.