论文标题
通量模块化，F理论和理性模型
Flux Modularity, F-Theory, and Rational Models
论文作者
论文摘要
在最近的工作中，我们猜想Calabi-yau三倍在$ \ mathbb {q} $上定义，并承认超对称通量压实是模块化的，并且与（tate tate tate tate tate tate tate tate）相关。在这项工作中，我们将解决两个自然的后续问题，即物理和数学性质，它们与之紧密相关。首先，从复杂的歧管转变为理性的多样性，就像研究模块化一样，我们暗中选择了三倍的“理性模型”。不同的理性模型选择如何影响我们的结果？其次，相同的模块化表格与$ \ mathbb {q} $上的椭圆曲线相关联；这些椭圆曲线是否在物理设置中的任何地方都找到？通过研究IIB字符串理论的超对称通量真空的F理论的提升（在$ \ Mathbb {p}（1,1,1,2,2,2,2）$中的Calabi-yau Hypersurface $ x $（1,1,2,2,2,2）$中，我们找到了与Elliptic Curves相关的EigigeN-eigigeN-egigeN匹配的纽约。实际上，我们发现了两个这样的家庭，它们对应于同一卡拉比Yaus家族的两个不同选择的理性模型。
In recent work, we conjectured that Calabi-Yau threefolds defined over $\mathbb{Q}$ and admitting a supersymmetric flux compactification are modular, and associated to (the Tate twists of) weight-two cuspidal Hecke eigenforms. In this work, we will address two natural follow-up questions, of both a physical and mathematical nature, that are surprisingly closely related. First, in passing from a complex manifold to a rational variety, as we must do to study modularity, we are implicitly choosing a "rational model" for the threefold; how do different choices of rational model affect our results? Second, the same modular forms are associated to elliptic curves over $\mathbb{Q}$; are these elliptic curves found anywhere in the physical setup? By studying the F-theory uplift of the supersymmetric flux vacua found in the compactification of IIB string theory on (the mirror of) the Calabi-Yau hypersurface $X$ in $\mathbb{P}(1,1,2,2,2)$, we find a one-parameter family of elliptic curves whose associated eigenforms exactly match those associated to $X$. Actually, we find two such families, corresponding to two different choices of rational models for the same family of Calabi-Yaus.
