Genus zero Gopakumar-Vafa invariants from open strings

TL;DR

This paper introduces a novel method to compute genus zero Gopakumar-Vafa invariants for certain non-toric Calabi-Yau threefolds using M-theory and string dualities, especially when traditional geometric resolutions are unavailable.

Contribution

It proposes a new approach leveraging dualities to define and compute invariants for non-toric, non-compact Calabi-Yau threefolds that lack small crepant resolutions.

Findings

GV invariants identified as five-dimensional open string zero modes

A new definition for genus zero GV invariants in non-resolvable threefolds

Non-geometric T-brane data often necessary for full invariant specification

Abstract

We propose a new way to compute the genus zero Gopakumar-Vafa invariants for two families of non-toric non-compact Calabi-Yau threefolds that admit simple flops: Reid's Pagodas, and Laufer's examples. We exploit the duality between M-theory on these threefolds, and IIA string theory with D6-branes and O6-planes. From this perspective, the GV invariants are detected as five-dimensional open string zero modes. We propose a definition for genus zero GV invariants for threefolds that do not admit small crepant resolutions. We find that in most cases, non-geometric T-brane data is required in order to fully specify the invariants.