# Stable pairs and Gopakumar-Vafa type invariants for Calabi-Yau 4-folds

## TL;DR

This paper introduces stable pair invariants for Calabi-Yau 4-folds, providing a new perspective on Gopakumar-Vafa type invariants and supporting their conjectured properties through computed examples.

## Contribution

It defines stable pair invariants for CY 4-folds and uses them to interpret and support the conjectured GV type invariants.

## Key findings

- Computed examples for compact CY 4-folds
- Supported integrality conjecture for GV type invariants
- Provided a new framework for understanding invariants in CY 4-folds

## Abstract

As an analogy to Gopakumar-Vafa conjecture on CY 3-folds, Klemm-Pandharipande defined GV type invariants on CY 4-folds using GW theory and conjectured their integrality. In this paper, we define stable pair type invariants on CY 4-folds and use them to interpret these GV type invariants. Examples are computed for both compact and non-compact CY 4-folds to support our conjectures.