Integrality structures in topological strings and quantum 2-functions. (English) Zbl 1522.81569
Summary: In this article, we first prove the integrality of an explicit disc counting formula obtained by M. Panfil and P. Sułkowski [J. High Energy Phys. 2019, No. 1, Paper No. 124, 45 p. (2019; Zbl 1409.83193)] 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 A. Schwarz et al. [Proc. Symp. Pure Math. 90, 113–128 (2015; Zbl 1356.81196)]. Finally, we provide a basic example of quantum 2-function and discuss the quantization of 2-functions.
MSC:
| 81T45 | Topological field theories in quantum mechanics |
| 14N35 | Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) |
| 57K16 | Finite-type and quantum invariants, topological quantum field theories (TQFT) |
Keywords:
differential and algebraic geometry; string duality; topological field theories; topological stringsReferences:
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