Mirror Maps, Modular Relations and Hypergeometric Series I

Details Mirror Maps, Modular Relations and Hypergeometric Series I Mirror Maps, Modular Relations and Hypergeometric Series I

1995-07-27

arxiv.org/abs/hep-th/9507151v1

Physics

High Energy Physics

High Energy Physics - Theory

24 pages; harvmac

Scientific paper

Motivated by the recent work of Kachru-Vafa in string theory, we study in Part A of this paper, certain identities involving modular forms, hypergeometric series, and more generally series solutions to Fuchsian equations. The identity which arises in string theory is the simpliest of its kind. There are nontrivial generalizations of the identity which appear new. We give many such examples -- all of which arise in mirror symmetry for algebraic K3 surfaces. In Part B, we study the integrality property of certain $q$-series, known as mirror maps, which arise in mirror symmetry.

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