Integrality theorems in the theory of topological strings
arXiv:0807.1714 · doi:10.1016/j.nuclphysb.2009.05.014
Abstract
We give a simplified derivation of the expression of instanton numbers and of mirror map in terms of Frobenius map on p-adic cohomology and use this expression to prove integrality theorems. Modifying this proof we verify that the Aganagic-Vafa formulas for the number of holomorphic disks can be expressed in terms of Frobenius map on p-adic relative cohomology; this expression permits us to prove integrality of this number.
33 pages, new results in the last section. Appendix added
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- Frobenius map for quintic threefolds
- Framing the Di-Logarithm (over Z)
- On the Arithmetic of D-brane Superpotentials. Lines and Conics on the Mirror Quintic
- Integrality of Framing and Geometric Origin of 2-functions
- Frobenius map on local Calabi-Yau manifolds