Integrality of instanton numbers and p-adic B-model

Maxim Kontsevich; Albert Schwarz; Vadim Vologodsky

doi:10.1016/j.physletb.2006.04.012

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Integrality of instanton numbers and p-adic B-model

Maxim Kontsevich·Albert Schwarz·Vadim Vologodsky

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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.

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Maxim Kontsevich, Albert Schwarz, Vadim Vologodsky. 2006-04-09. Integrality of instanton numbers and p-adic B-model. https://doi.org/10.1016/j.physletb.2006.04.012

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