发表机构
Institute for Mathematical Informatics, Meiji Gakuin University（明治学院大学数学信息研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文确定了与带Wilson线的heterotic弦理论对偶的F理论背景，用正交模形式表达椭圆曲线，并证明其标度极限给出E-弦理论的Seiberg-Witten曲线，同时猜想该结果提供了K3曲面的显式逆周期映射。
AI 中文摘要
我们确定了与在$T^2$上紧致化且对两个$E_8$之一开启一般Wilson线的heterotic弦理论对偶的精确F理论背景。描述这些背景的椭圆曲线用正交模形式表达，并确定其允许一个非平凡标度极限，从而产生一个有理椭圆曲面。我们确认在该极限下，该曲线约化为E-弦理论的Seiberg-Witten曲线。我们猜想，我们的结果为以$U\oplus E_8(-1)$格极化的代数K3曲面给出了一个显式的逆周期映射。
英文摘要
We identify the precise F-theory backgrounds dual to the heterotic string theory compactified on $T^2$ with general Wilson lines turned on for one of the two $E_8$'s. The elliptic curve describing the backgrounds is expressed in terms of orthogonal modular forms and is determined so that it admits a nontrivial scaling limit yielding a rational elliptic surface. We confirm that the curve reduces to the Seiberg-Witten curve for the E-string theory in this limit. We conjecture that our result gives an explicit inverse period map for algebraic K3 surfaces polarized by the $U\oplus E_8(-1)$ lattice.
Comments17 pages, 2 ancillary files
