Some remarks on Gopakumar-Vafa invariants

TL;DR

This paper presents a new way to express Gopakumar-Vafa invariants using the cohomology ring of D-brane moduli spaces, avoiding the need for the sl_2 imes sl_2 action, and provides a straightforward construction of this action.

Contribution

It introduces a novel expression for Gopakumar-Vafa invariants based on cohomology rings, simplifying previous approaches that relied on the sl_2 imes sl_2 action.

Findings

Gopakumar-Vafa invariants can be expressed via cohomology rings

A simple construction of the sl_2 imes sl_2 action is provided

The approach simplifies the understanding of invariants in string theory

Abstract

We show that Gopakumar-Vafa invariants can be expressed in terms of the cohomology ring of moduli space of D-branes without reference to the sl_2 \times sl_2 action. We also give a simple construction of this action.