$E_n$Jacobi形式与Seiberg–Witten曲线

IF 1.2 3区数学 Q1 MATHEMATICS

Communications in Number Theory and Physics Pub Date : 2017-06-14 DOI:10.4310/CNTP.2019.v13.n1.a2

K. Sakai

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引用次数: 17

摘要

讨论了E_n (n=6,7,8)型Weyl群作用下的Jacobi型不变量。对于n=6,7，我们显式构造了E_n弱Jacobi形式代数的完整生成集。我们首先用雅可比函数和模形式构造n+1个独立的E_n雅可比形式。利用它们，我们得到了e弦理论的E_6型和E_7型Seiberg-Witten曲线。每条曲线的系数都是由根系指定的特定权值和指标的E_n个弱雅可比形式，实现了Wirthm\ uller在前段时间所证明的产生子。

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$E_n$ Jacobi forms and Seiberg–Witten curves

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.

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来源期刊

Communications in Number Theory and Physics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.70

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： Focused on the applications of number theory in the broadest sense to theoretical physics. Offers a forum for communication among researchers in number theory and theoretical physics by publishing primarily research, review, and expository articles regarding the relationship and dynamics between the two fields.