Integrality of instanton numbers and p-adic B-model

TL;DR

This paper proves the integrality of genus zero Gopakumar-Vafa invariants for Calabi-Yau manifolds using p-adic cohomology and Frobenius maps, extending results from one-dimensional moduli spaces to the general case.

Contribution

It introduces a method to establish the integrality of instanton numbers for Calabi-Yau manifolds via p-adic cohomology and Frobenius maps, applicable to general moduli spaces.

Findings

Proves integrality of instanton numbers for quintic and other Calabi-Yau manifolds.

Expresses instanton numbers in terms of Frobenius map on p-adic cohomology.

Extends integrality proof from one-dimensional to general moduli spaces.

Abstract

We study integrality of instanton numbers (genus zero Gopakumar - Vafa invariants) for quintic and other Calabi-Yau manifolds. We start with the analysis of the case when the moduli space of complex structures is one-dimensional; later we show that our methods can be used to prove integrality in general case. We give an expression of instanton numbers in terms of Frobenius map on $p$-adic cohomology ; the proof of integrality is based on this expression.