Integrality of open instantons numbers

JOURNAL OF GEOMETRY AND PHYSICS

卷:52

Article

Grünberg, DB

关键词: open instantons;    enumerative geometry;    Gromow-Witten invariants;    integrality of BPS invariants;    Wolstenholme and Wilson theorems;   

DOI  :  10.1016/j.geomphys.2004.03.004

来源: Elsevier

【 摘 要 】

We prove the integrality of the open instanton numbers in two examples of counting holomorphic disks on local Calabi-Yau three-folds: the resolved conifold and the degenerate P-1 x P-1. Given the B-model superpotential, we extract by hand all Gromow-Witten invariants in the expansion of the A-model superpotential. The proof of their integrality relies on enticing congruences of binomial coefficients modulo powers of a prime. We also derive an expression for the factorial (p(k) - 1)! modulo powers of the prime p. We generalise two theorems of elementary number theory, by Wolstenholme and Wilson. (C) 2004 Elsevier B.V. All rights reserved.

【 授权许可】

Free