Integrality of instanton numbers and p-adic B-model
- Author(s): Kontsevich, Maxim;
- Schwarz, Albert;
- Vologodsky, Vadim
- et al.
Published Web Locationhttps://arxiv.org/pdf/hep-th/0603106.pdf
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.