Exploring infinite distance limits of type II Calabi–Yau compactifications

This thesis explores infinite distance limits in the vector multiplet moduli space of type II string theory on Calabi–Yau threefolds. First we classify such limits, identify the towers of light states, and test the Emergence Proposal, which links IR kinetic terms to loop corrections from such states. We then study the scalar curvature of the moduli space along infinite distance trajectories, focusing on cases where it diverges positively. We argue that such divergences signal decoupled field theory sectors and propose this as the only mechanism for curvature divergences in quantum gravity. Extending the analysis, we relate these limits to higher-dimensional rigid theories (5d/6d SCFTs and Little String Theories), interpreting divergences as a parametric separation between the strength of gravitational and gauge interactions. Finally, we connect curvature divergences with rigid limits and the existence of BPS states with divergent charge-to-mass ratios.