Elliptically fibered Calabi-Yau manifolds and the ring of Jacobi forms

Min xin Huang, Sheldon Katz, Albrecht Klemm

Research output: Contribution to journalArticlepeer-review


We give evidence that the all genus amplitudes of topological string theory on compact elliptically fibered Calabi-Yau manifolds can be written in terms of meromorphic Jacobi forms whose weight grows linearly and whose index grows quadratically with the base degree. The denominators of these forms have a simple universal form with the property that the poles of the meromorphic form lie only at torsion points. The modular parameter corresponds to the fibre class while the role of the string coupling is played by the elliptic parameter. This leads to very strong all genus results on these geometries, which are checked against results from curve counting.

Original languageEnglish (US)
Pages (from-to)681-692
Number of pages12
JournalNuclear Physics B
StatePublished - Sep 1 2015

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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