In this study, we construct four-dimensional F-theory models with 3 to 8 U(1) factors on products of K3 surfaces. We provide explicit Weierstrass equations of elliptic K3 surfaces with Mordell–Weil ranks of 3 to 8. We utilize the method of quadratic base change to glue pairs of rational elliptic surfaces together to yield the aforementioned types of K3 surfaces. The moduli of elliptic K3 surfaces constructed in the study include Kummer surfaces of specific complex structures. We show that the tadpole cancels in F-theory compactifications with flux when these Kummer surfaces are paired with appropriately selected attractive K3 surfaces. We determine the matter spectra on F-theory on the pairs.

中文翻译：

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在 K3 表面上具有 3 到 8 个 U(1) 因子的 F 理论模型

在这项研究中，我们在 K3 曲面的产品上构建了具有 3 到 8 个 U(1) 因子的四维 F 理论模型。我们提供了具有 3 到 8 阶的 Mordell-Weil 等级的椭圆 K3 曲面的显式 Weierstrass 方程。我们利用二次基数变化的方法将有理椭圆曲面对粘合在一起以产生上述类型的 K3 曲面。研究中构建的椭圆K3曲面的模量包括特定复杂结构的Kummer曲面。We show that the tadpole cancels in F-theory compactifications with flux when these Kummer surfaces are paired with appropriately selected attractive K3 surfaces. 我们在对上确定了 F 理论的物质光谱。