Integrality theorems in the theory of topological strings

Details Integrality theorems in the theory of topological strings Integrality theorems in the theory of topological strings

2008-07-10

arxiv.org/abs/0807.1714v2

Nucl.Phys.B821:506-534,2009

Physics

High Energy Physics

High Energy Physics - Theory

33 pages, new results in the last section. Appendix added

Scientific paper

10.1016/j.nuclphysb.2009.05.014

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.

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