F-理论中的连续$E_7\times E_7$非几何杂化弦、稳定退化和增强规范群
Unbroken $E_7\times E_7$ nongeometric heterotic strings, stable degenerations and enhanced gauge groups in F-theory duals
摘要：
Malmendier和Morrison构造了规范代数为$\mathfrak{e}_8\mathfrak{e}_7$的八维非几何杂化弦，作为$Λ^{1,1}\oplus E_8\oplus E_7$晶格极化的K3面上F理论的杂化弦. Clingher，Malmendier和Shaska将这些构造推广到八维非几何杂化弦，其中规范代数$\mathfrak{e}_7\mathfrak{e}_7$作为$Λ^{1,1}\oplus E_7\oplus E_7$格点极化K3面上F-理论的杂化代数。在本研究中，我们用规范代数$\mathfrak{e}_7\mathfrak{e}_7$分析了非几何杂化弦模中的点，在这些点处F-理论侧的非阿贝尔规范群得到最大增强。杂种优势侧的规范群不允许在这些点上进行微扰解释。我们表明，这些理论可以被描述为变形的稳定退化，作为一致的7膜的F-理论的一面。从杂种优势的观点来看，这种效应对应于5-膜的插入。这些效应可以用来理解非几何杂化弦的非微扰方面。此外，我们通过在$\mathbb{P}^1$上用规范代数$\mathfrak{e}_7\mathfrak{e}_7$构造属于非几何杂化弦模的F-理论侧的椭圆K3曲面，建立了一族椭圆Calabi-Yau 3-折叠.我们发现，高度增强的规范对称性出现在F-理论上的椭圆卡-丘3-折叠。
英文摘要：
Eight-dimensional non-geometric heterotic strings with gauge algebra $\mathfrak{e}_8\mathfrak{e}_7$ were constructed by Malmendier and Morrison as heterotic duals of F-theory on K3 surfaces with $Λ^{1,1}\oplus E_8\oplus E_7$ lattice polarization. Clingher, Malmendier and Shaska extended these constructions to eight-dimensional non-geometric heterotic strings with gauge algebra $\mathfrak{e}_7\mathfrak{e}_7$ as heterotic duals of F-theory on $Λ^{1,1}\oplus E_7\oplus E_7$ lattice polarized K3 surfaces. In this study, we analyze the points in the moduli of non-geometric heterotic strings with gauge algebra $\mathfrak{e}_7\mathfrak{e}_7$, at which the non-Abelian gauge groups on the F-theory side are maximally enhanced. The gauge groups on the heterotic side do not allow for the perturbative interpretation at these points. We show that these theories can be described as deformations of the stable degenerations, as a result of coincident 7-branes on the F-theory side. From the heterotic viewpoint, this effect corresponds to the insertion of 5-branes. These effects can be used to understand nonperturbative aspects of nongeometric heterotic strings. Additionally, we build a family of elliptic Calabi-Yau 3-folds by fibering elliptic K3 surfaces, which belong to the F-theory side of the moduli of non-geometric heterotic strings with gauge algebra $\mathfrak{e}_7\mathfrak{e}_7$, over $\mathbb{P}^1$. We find that highly enhanced gauge symmetries arise on F-theory on the built elliptic Calabi-Yau 3-folds.
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