Quantum obstructions for $N=1$ infinite distance limits -- Part II: K\"ahler obstructions

Abstract

We continue our analysis of quantum corrections in the complex structure moduli space of four-dimensional Type IIB/F-theory compactifications with N=1 supersymmetry. We find that limits in the complex structure moduli space of F-theory generically induce a strong backreaction on other sectors of the theory, reflecting the non-factorisation of the field space in genuine $N=1$ theories at the quantum level. Our focus is on quantum corrections to the K\"ahler moduli in F-theory on Calabi-Yau fourfolds and proceeds in two independent ways: A detailed analysis of the worldsheet theory of candidate EFT strings for pure complex structure infinite distance limits reveals a mismatch with expectations based on the classical effective action and points to a quantum obstruction of the limit. Complementary to this, we confirm, in large classes of theories, the existence of significant complex structure dependent quantum corrections to the action of BPS instantons which at tree-level are governed by the K\"ahler moduli. As the quantum corrections become uncontrolled at large complex structure, they require a co-scaling of the K\"ahler moduli to maintain perturbative control. As a result, the naive, classical effective action does not provide an accurate description of pure large complex structure regimes. We comment on possible implications for string phenomenology, specifically with regard to model building and moduli stabilisation.