Integrality structures in topological strings and quantum 2-functions

In this article, we first prove the integrality of an explicit disc counting formula obtained by Panfil and Sulkowski for a class of toric Calabi-Yau manifolds named generalized conifolds. Then, motivated by the integrality structures in open topological string theory, we introduce a mathematical notion of quantum 2-function which can be viewed as the quantization of the notion of 2-function introduced by Schwarz, Vologodsky and Walcher. Finally, we provide a basic example of quantum 2-function and discuss the quantization of 2-functions.

Automated summary

In this article, the integrality of an explicit disc counting formula for toric Calabi-Yau manifolds called generalized conifolds is proven. A mathematical notion of quantum 2-function is introduced, which is a quantization of the notion of 2-function introduced by Schwarz, Vologodsky, and Walcher. A basic example of quantum 2-function is provided and the quantization of 2-functions is discussed.