We investigate gauge theories and matter contents in F-theory compactifications on families of genus-one fibered Calabi-Yau 4-folds lacking a global section. To construct families of genus-one fibered Calabi-Yau 4-folds that lack a global section, we consider two constructions: hypersurfaces in a product of projective spaces, and double covers of a product of projective spaces. We consider specific forms of defining equations for these genus-one fibrations, so that genus-one fibers possess complex multiplications of specific orders. These symmetries enable a detailed analysis of gauge theories. $E_6$, $E_7$, and $SU(5)$ gauge groups arise in some models. Discriminant components intersect with one another in the constructed models, and therefore, discriminant components contain matter curves. We deduce potential matter spectra and Yukawa couplings.

中文翻译：

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$F$ 中的规范群和物质光谱 - 属一纤维 Calabi-Yau 的理论紧缩 $4$ - 无截面折叠：超曲面和双盖结构

我们研究了缺乏全局截面的 1 属纤维 Calabi-Yau 4 倍家族的 F 理论紧缩中的规范理论和物质含量。为了构造缺乏全局截面的属一纤维化 Calabi-Yau 4-fold 的族，我们考虑两种构造：射影空间乘积中的超曲面和射影空间乘积的双覆盖。我们考虑定义这些第一类纤维的方程的特定形式，因此第一类纤维具有特定阶次的复杂乘法。这些对称性使得能够对规范理论进行详细分析。$E_6$、$E_7$ 和 $SU(5)$ 仪表组出现在某些模型中。判别分量在构建的模型中相互交叉，因此判别分量包含物质曲线。我们推导出势物质谱和汤川耦合。