双覆盖上无截面紧化的F-理论模型的规范对称性和物质场及费马四次K3乘K3构造
Gauge symmetries and matter fields in F-theory models without section- compactifications on double cover and Fermat quartic K3 constructions times K3
摘要：
本文研究了在没有整体截面的亏格纤维卡-丘4-折叠上的F-理论紧化中的规范理论和物质场。在这项研究中，一类纤维卡-丘4-折叠被构建为一类纤维K3表面的直接产物，该表面缺乏截面乘以K3表面。考虑$\mathbb{P}^1\times\mathbb{P}^1$沿二次（4，4）曲线分歧的双覆盖，以及$\mathbb{P}^1\times\mathbb{P}^3$中两个二次（1，2）超曲面的完全交，构造了一类无截面的纤维K3曲面. $E_7$规范群产生于双覆盖时间K3上的某些F-理论紧化。我们证明了当完全交K3同构于Fermat四次曲面时，在完全交K3乘K3上的F-理论紧化的蝌蚪可以被消去，并且在直积中适当地选择了另一个K3曲面的复结构.
英文摘要：
We investigate gauge theories and matter fields in F-theory compactifications on genus-one fibered Calabi-Yau 4-folds without a global section. In this study, genus-one fibered Calabi-Yau 4-folds are built as direct products of a genus-one fibered K3 surface that lacks a section times a K3 surface. We consider i) double covers of $\mathbb{P}^1\times\mathbb{P}^1$ ramified along a bidegree (4,4) curve, and ii) complete intersections of two bidegree (1,2) hypersurfaces in $\mathbb{P}^1\times\mathbb{P}^3$ to construct genus-one fibered K3 surfaces without a section. $E_7$ gauge group arises in some F-theory compactifications on double covers times K3. We show that the tadpole can be cancelled for an F-theory compactification on complete intersection K3 times K3, when complete intersection K3 is isomorphic to the Fermat quartic, and the complex structure of the other K3 surface in the direct product is appropriately chosen.
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