F-理论紧化中的四面体
Tetrahedron in F-theory Compactification
摘要：
复四面体曲面$\mathcal{T}$是由四个相交的复射影平面$CP^{2}$生成的非平面射影曲面。本文研究了$\mathcal{T}$的爆破族$\{\mathcal{T}_{m}\} $，并证明了这些$\mathcal{T}_{m}$与通过爆破$CP^{2}$中的n个孤立点得到的del Pezzo曲面集$dP_{n}$之间的联系. $\mathcal{T}_{m}$是表现出$U(1) \times U(1) $对称性的复曲面，其可用于设计Beasley-Heckman-Vafa理论中的规范对称性增强。四面体的放大具有环面图，其具有面、边和顶点，其中可以分别将场局部化在伴随表示、手征物质和汤川三场耦合中，这是F理论GUT模型构建的工程所需的。
英文摘要：
Complex tetrahedral surface $\mathcal{T}$ is a non planar projective surface that is generated by four intersecting complex projective planes $CP^{2}$. In this paper, we study the family $\{\mathcal{T}_{m}\} $ of blow ups of $\mathcal{T}$ and exhibit the link of these $\mathcal{T}_{m}$s with the set of del Pezzo surfaces $dP_{n}$ obtained by blowing up n isolated points in the $CP^{2}$. The $\mathcal{T}_{m}$s are toric surfaces exhibiting a $U(1) \times U(1) $ symmetry that may be used to engineer gauge symmetry enhancements in the Beasley-Heckman-Vafa theory. The blown ups of the tetrahedron have toric graphs with faces, edges and vertices where may localize respectively fields in adjoint representations, chiral matter and Yukawa tri-fields couplings needed for the engineering of F- theory GUT models building.
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