具有$\mathbb{Z}_2$宇称的手征MSSM的F理论实现
An F-theory Realization of the Chiral MSSM with $\mathbb{Z}_2$-Parity
摘要：
为了禁止所有四维重子和轻子数违反算符，我们利用F理论构造了具有标准模型规范群、三个手征代和物质宇称的四维${\cal N}=1$ SUGRA理论.基本的几何结构是通过构造光滑的属一纤维卡拉比-丘四倍使用环面顶部，有一个雅可比纤维与秩一Mordell-Weil群和$SU(3) \times SU(2) $奇点。光滑四重上的必要规范背景被证明是完全兼容的量子化条件，包括正整数D3-蝌蚪。这种构造首次实现了F理论中具有物质宇称的MSSM类模型的一致UV完备化。此外，我们的结构是一般性的，也表现出其他相关的$\mathbb{Z}_2$收费扩展的MSSM，如轻子和重子宇称。然而，这样的模型呈现不一致的非整数通量，这是必要的，以产生精确的MSSM手性光谱。这些不一致的结果是密切相关的场论考虑到紫外线嵌入的$\mathbb{Z}_2$到一个$U(1)$和由此产生的离散异常。
英文摘要：
Using F-theory we construct 4D ${\cal N}=1$ SUGRA theories with the Standard Model gauge group, three chiral generations, and matter parity in order to forbid all dimension four baryon and lepton number violating operators. The underlying geometries are derived by constructing smooth genus-one fibered Calabi--Yau fourfolds using toric tops that have a Jacobian fibration with rank one Mordell--Weil group and $SU(3) \times SU(2) $ singularities. The necessary gauge backgrounds on the smooth fourfolds are shown to be fully compatible with the quantization condition, including positive integer D3-tadpoles. This construction realizes for the first time a consistent UV completion of an MSSM-like model with matter parity in F-theory. Moreover our construction is general enough to also exhibit other relevant $\mathbb{Z}_2$ charge extensions of the MSSM such as lepton and baryon parity. Such models however are rendered inconsistent by non-integer fluxes, which are necessary for producing the exact MSSM chiral spectrum. These inconsistencies turn out to be intimately related to field theory considerations regarding a UV-embedding of the $\mathbb{Z}_2$ into a $U(1)$ and the resulting discrete anomalies.
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