Luca Melotti - The moduli space curvature and the Weak Gravity Conjecture

We discuss a remarkable interplay between rigid field theories (RFTs), charge-to-mass ratios and scalar curvature divergences in the vector multiplet moduli space of 4d N = 2 supergravities, obtained upon compactifying type II string theory on Calabi–Yau threefolds. We show that the condition to obtain an RFT sector that decouples from gravity implies a divergence in the charge-to-mass ratio of (would-be) BPS particles charged under the rigid theory, and vice-versa. For weak coupling limits where the scalar curvature of the moduli space diverges, we argue that such BPS particles exist and relate their charge-to-mass ratios to the curvature divergence and argue that all these divergences are a consequence of RFT limits.