Quantum obstructions for $N=1$ infinite distance limits -- Part I: $g_s$ obstructions

We analyse quantum obstructions to classical infinite distance limits in four-dimensional string compactifications with N=1 supersymmetry. Such quantum effects signal a severe departure from the perturbative effective action and can be of considerable importance for string model building. Our focus is on the complex structure moduli space of Type IIB orientifolds with O7/O3-planes and its F-theory description. In this first part of our analysis, we investigate the behaviour of $g_s$ corrections in infinite distance complex structure limits. Our main finding is that, depending on the location of the O7-plane, non-perturbative corrections in $g_s$ can become unsuppressed, thus obstructing a perturbative Type IIB description in the corresponding asymptotic region of the field space. In particular, this applies to large complex structure limits. To show this, we study the F-theory description of the Type IIB orientifold, in which all pure $g_s$ corrections are encoded in the (classical) geometry of an elliptic Calabi-Yau fourfold. This $g_s$-corrected moduli space is found to differ significantly from the classical moduli space. In extreme cases the classical infinite distance degeneration can be completely removed at the $g_s$-corrected quantum level. The behaviour of $\alpha'$ corrections, as well as implications for string model building, are discussed in a companion paper.