Gromov-Witten invariants and membrane indices of fivefolds via the topological vertex

TL;DR

This paper introduces a conjecture about almost integer invariants for Gromov-Witten theory of Calabi-Yau fivefolds with torus actions, proves it for specific cases using a topological vertex formalism, and demonstrates applications through examples.

Contribution

It proposes a new conjecture on invariants in Gromov-Witten theory and develops a vertex formalism to evaluate these invariants for certain fivefolds.

Findings

Conjecture on almost integer invariants for Calabi-Yau fivefolds.

Vertex formalism evaluation of Gromov-Witten invariants.

Validation of the formalism through multiple examples.

Abstract

We conjecture the existence of almost integer invariants governing the all-genus equivariant Gromov-Witten theory of Calabi-Yau fivefolds with a torus action. We prove the conjecture for skeletal, locally anti-diagonal torus actions by establishing a vertex formalism evaluating the Gromov-Witten invariants via the topological vertex of Aganagic, Klemm, Marino and Vafa. We apply the formalism in several examples.