复曲面F理论中的几何工程和U（1）规范因子的大统一理论
Geometric Engineering in Toric F-Theory and GUTs with U(1) Gauge Factors
摘要：
本文给出了一种算法，在给定的基和规范群下，系统地构造出复曲面环境空间中所有实现为超曲面的Calabi-Yau椭圆纤维化。这种一般方法被应用于构造具有多个U（1）规范因子的SU（5）大统一理论的特殊问题。基本数据包括一个顶部的每个环面因子在基地连同紧化数据给嵌入到一个自反多面体。紧化数据的允许选择是辅助多面体中的整点。为了保证低能规范理论的存在性，椭圆纤维化必须是平坦的，这被重新表述为顶部及其嵌入的条件。特别地，SU（5）四重的平坦性对紧化的辅助多面体施加了额外的线性约束，因此是非一般的。系统地研究了复曲面F-理论紧化中的阿贝尔规范对称性。与每个顶点相关联，计算确定U（1）因子的最小数量的复曲面Mordell-Weil群。此外，所有的SU（5）-顶和它们的分裂类型被确定，并用于推断U（1）物质电荷的模式。
英文摘要：
An algorithm to systematically construct all Calabi-Yau elliptic fibrations realized as hypersurfaces in a toric ambient space for a given base and gauge group is described. This general method is applied to the particular question of constructing SU(5) GUTs with multiple U(1) gauge factors. The basic data consists of a top over each toric divisor in the base together with compactification data giving the embedding into a reflexive polytope. The allowed choices of compactification data are integral points in an auxiliary polytope. In order to ensure the existence of a low-energy gauge theory, the elliptic fibration must be flat, which is reformulated into conditions on the top and its embedding. In particular, flatness of SU(5) fourfolds imposes additional linear constraints on the auxiliary polytope of compactifications, and is therefore non-generic. Abelian gauge symmetries arising in toric F-theory compactifications are studied systematically. Associated to each top, the toric Mordell-Weil group determining the minimal number of U(1) factors is computed. Furthermore, all SU(5)-tops and their splitting types are determined and used to infer the pattern of U(1) matter charges.
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