Integrality of instanton numbers and p-adic B-model

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.

10 pages, minor changes

References in corpus (3)

• Mirror Symmetry For Zeta Functions
• Integrality of instanton numbers
• Supergeometry and Arithmetic Geometry

Cited by in corpus (6)

• Twisted de Rham cohomology, homological definition of the integral and "Physics over a ring"
• Integrality theorems in the theory of topological strings
• Supergeometry and Arithmetic Geometry
• Frobenius transformation, mirror map and instanton numbers
• Frobenius map on local Calabi-Yau manifolds
• Quantum Extended Arithmetic Veneziano Amplitude