Unbroken $E7 \times E7$ nongeometric heterotic strings, stable degenerations and enhanced gauge groups in F-theory duals

Eight-dimensional non-geometric heterotic strings with gauge algebra $\mathfrak{e}_8\mathfrak{e}_7$ were constructed by Malmendier and Morrison as duals of F-theory on K3 surfaces $\Lambda^{1,1}\oplus E_8\oplus E_7$ lattice polarization. Clingher, Shaska extended these constructions to eight-dimensional $\mathfrak{e}_7\mathfrak{e}_7$ E_7\oplus polarized surfaces. In this study, we analyze the points in moduli $\mathfrak{e}_7\mathfrak{e}_7$, at which non-Abelian groups side are maximally enhanced. The do not allow for perturbative interpretation points. We show that theories can be described deformations stable degenerations, a result coincident 7-branes side. From viewpoint, effect corresponds insertion 5-branes. These effects used understand nonperturbative aspects nongeometric strings. Additionally, build family elliptic Calabi-Yau 3-folds fibering surfaces, belong over $\mathbb{P}^1$. find highly enhanced symmetries arise built 3-folds.