F-理论与一切理性：用理性截面考察U（1）对称
F-theory and All Things Rational: Surveying U(1) Symmetries with Rational Sections
摘要：
我们研究了F-理论紧化的椭圆纤维化，实现了具有阿贝尔规范因子的4d和6d超对称规范理论。在纤维化中，这些U（1）对称性是通过附加的有理截面来实现的。通过确定两个有理截面纤维的余维，得到了物质场所有可能的U（1）荷的普适刻画。考虑到超对称大统一理论的建模，我们分析的主要例子之一是SU（5）规范理论与\bar{5}和10物质的U（1）对称性。我们使用卡-丘三重和四重有理曲线的法向丛上的约束组合，以及在余维2中纤维中有理曲线的分裂，来确定光滑有理截面的可能配置。这种分析直接推广到多个U（1）。我们研究了这种纤维的触发器，以及一些余维3的汤川耦合。此外，我们进行了一个普遍的研究U（1）-荷GUT单态，包括他们的KK-电荷，并确定所有实现的单态纤维。通过对这些单态赋予真空期望值，我们提出了一种系统的方法来分析U（1）s到F理论中离散规范对称性的希格斯辛。
英文摘要：
We study elliptic fibrations for F-theory compactifications realizing 4d and 6d supersymmetric gauge theories with abelian gauge factors. In the fibration these U(1) symmetries are realized in terms of additional rational sections. We obtain a universal characterization of all the possible U(1) charges of matter fields by determining the corresponding codimension two fibers with rational sections. In view of modelling supersymmetric Grand Unified Theories, one of the main examples that we analyze are U(1) symmetries for SU(5) gauge theories with \bar{5} and 10 matter. We use a combination of constraints on the normal bundle of rational curves in Calabi-Yau three- and four-folds, as well as the splitting of rational curves in the fibers in codimension two, to determine the possible configurations of smooth rational sections. This analysis straightforwardly generalizes to multiple U(1)s. We study the flops of such fibers, as well as some of the Yukawa couplings in codimension three. Furthermore, we carry out a universal study of the U(1)-charged GUT singlets, including their KK-charges, and determine all realizations of singlet fibers. By giving vacuum expectation values to these singlets, we propose a systematic way to analyze the Higgsing of U(1)s to discrete gauge symmetries in F-theory.
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