E_n Jacobi forms and Seiberg-Witten curves
High Energy Physics - Theory
2019-05-01 v3 Algebraic Geometry
Number Theory
Abstract
We discuss Jacobi forms that are invariant under the action of the Weyl group of type E_n (n=6,7,8). For n=6,7 we explicitly construct a full set of generators of the algebra of E_n weak Jacobi forms. We first construct n+1 independent E_n Jacobi forms in terms of Jacobi theta functions and modular forms. By using them we obtain Seiberg-Witten curves of type E_6 and E_7 for the E-string theory. The coefficients of each curve are E_n weak Jacobi forms of particular weights and indices specified by the root system, realizing the generators whose existence was shown some time ago by Wirthm\"uller.
Cite
@article{arxiv.1706.04619,
title = {E_n Jacobi forms and Seiberg-Witten curves},
author = {Kazuhiro Sakai},
journal= {arXiv preprint arXiv:1706.04619},
year = {2019}
}
Comments
24 pages, 1 figure, v2: refined discussion in section 3, v3: published version