KEK-TH-2094

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

1.2cm

Yusuke Kimura$^1$ 0.4cm [*$^1$KEK Theory Center, Institute of Particle and Nuclear Studies, KEK,\
1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan*]{} 0.4cm E-mail: kimurayu@post.kek.jp

1.5cm

Introduction
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F-theory/heterotic duality [@Vaf; @MV1; @MV2; @Sen; @FMW] states that F-theory [@Vaf; @MV1; @MV2] compactification on an elliptic K3 fibered Calabi–Yau $(n+1)$-fold describes a theory physically equivalent to heterotic compactification[^1] on an elliptic Calabi–Yau $n$-fold. Non-perturbative aspects of heterotic theory can be studied by utilizing this duality. F-theory/heterotic duality is strictly formulated when the stable degeneration limit[^2] [@FMW; @AM] is taken on the F-theory side in which K3 fibers split into pairs of half K3 surfaces.

Recently, eight-dimensional non-geometric heterotic strings with unbroken $\mathfrak{e}_8\mathfrak{e}_7$ algebra were constructed by Malmendier and Morrison [@MM] by utilizing the F-theory/heterotic duality. The Narain space [@Narain] $$D_{2,18} / O(\Lambda^{2,18})$$ gives the moduli space of eight-dimensional heterotic strings, and the double cover of this space, $$D_{2,18} / O^+ (\Lambda^{2,18}),$$ is equivalent to the moduli space of F-theory on elliptic K3 surfaces with a section. This is the statement of F-theory/heterotic duality. Malmendier and Morrison considered F-theory compactifications on elliptic K3 surfaces with $H\oplus E_8\oplus E_7$ 