  We consider 4d N=1 theories arising from F-theory compactifications on
elliptically-fibered Calabi-Yau four-folds and investigate the non-perturbative
structure of their scalar field space beyond the large volume/large complex
structure regime. We focus on regimes where the F-theory field space
effectively reduces to the deformation space of the worldsheet theory of a
critical string obtained from a wrapped D3-brane. In case that this critical
string is a heterotic string with a simple GLSM description, we identify new
strong coupling singularities in the interior of the F-theory field space.
Whereas from the perturbative perspective these singularities manifest
themselves through a breakdown of the perturbative $\alpha'$-expansion, the
dual GLSM perspective reveals that at the non-perturbative level these
singularities correspond to loci in field space along which the worldsheet
theory of the critical D3-brane string breaks down and a 7-brane gauge theory
becomes strongly coupled due to quantum effects. Therefore these singularities
signal a transition to a strong coupling phase in the F-theory field space
which can be shown to arise due to the failure of the F-theory field space to
factorize between complex structure and Kahler sector at the quantum level.
Such singularities are hence a feature of a genuine N=1 theory without a direct
counterpart in N=2 theories in 4d. By relating our setup to recent studies of
global string solutions associated to axionic strings we argue that the
D3-brane string dual to the perturbative heterotic string leaves the spectrum
of BPS strings when traversing into the strong coupling phase. The absence of
the perturbative, critical heterotic string then provides a physical
explanation for the breakdown of the perturbative expansion and the obstruction
of certain classical infinite distance limits in accordance with the Emergent
String Conjecture.
