English

Integrality theorems in the theory of topological strings

High Energy Physics - Theory 2009-09-28 v2

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.

Cite

@article{arxiv.0807.1714,
  title  = {Integrality theorems in the theory of topological strings},
  author = {Albert Schwarz and Vadim Vologodsky},
  journal= {arXiv preprint arXiv:0807.1714},
  year   = {2009}
}

Comments

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

R2 v1 2026-06-21T10:59:24.167Z