Unbroken $E_7\times E_7$ nongeometric heterotic strings, stable degenerations and enhanced gauge groups in F-theory duals

Abstract

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 ${\Lambda }^{1,1}\oplus E_8\oplus E_7$ 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 ${\Lambda }^{1,1}\oplus E_7\oplus E_7$ 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.

47 pages. Minor changes in section 4.4 and section 5

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Cited by in corpus (8)

• Discrete gauge groups in certain F-theory models in six dimensions
• Charge completeness and the massless charge lattice in F-theory models of supergravity
• The duality between F-theory and the Heterotic String in $D=8$ with two Wilson lines
• F-theory models with 3 to 8 U(1) factors on K3 surfaces
• Magic square and half-hypermultiplets in F-theory
• Types of gauge groups in six-dimensional F-theory on double covers of rational elliptic 3-folds
• Eight-dimensional non-geometric heterotic strings and enhanced gauge groups
• Four-dimensional $\mathcal{N}=1$ SCFTs on S-folds with T-branes and AdS/CFT correspondence