to the points in the moduli of eight-dimensional non-geometric heterotic strings on the 2-torus $T^2$ constructed in [@CMSE7], at which the ranks of the non-Abelian gauge groups are enhanced to 18 on the F-theory side. These are the maximal enhancements of the non-Abelian gauge groups on the F-theory side. We mainly consider $E_8\times E_8$ heterotic strings, rather than $SO(32)$ heterotic strings. (However, we do consider some applications to $SO(32)$ heterotic strings.) As only up to an $E_8\times E_8 \times U(1)^4$ gauge group can arise in eight-dimensional $E_8 \times E_8$ heterotic strings compactified on the 2-torus [@Kimura1810], a consideration of the ranks of the non-Abelian gauge groups reveals that the gauge groups of the dual heterotic theories of these F-theory models do not allow for a perturbative interpretation. These heterotic strings include the non-perturbative effects of 5-branes. We find that these theories can be described as the deformations of the heterotic strings from the stable degeneration limit, in which the F-theory/heterotic duality strictly holds, and that these deformations result from the coincident 7-branes on the F-theory side. In the heterotic language, the effect of coincident 7-branes corresponds to the presence of 5-branes.

When the non-Abelian gauge groups on F-theory on an 