Minimal Weak Gravity Conjecture and gauge duality in M-theory on K3 ×T²

The minimal Weak Gravity Conjecture (WGC) predicts the emergence of towers of superextremal states in both weak and strong coupling limits. In this work, we study M-theory compactified on a special class of Calabi-Yau threefolds to construct a 5D effective field theory (EFT) that accommodates both weak and strong gauge coupling limits. Building on a classification of fiber structures of Calabi-Yau threefolds with finite volume, we establish a correspondence between curves in the fiber and the base, which relates weak and strong gauge couplings. This allows us to probe non-perturbative effects by treating strong couplings through their weakly counterparts. We use this result and properties of Bogomol'nyi--Prasad--Sommerfield (BPS) states to demonstrate that M-theory on such Calabi-Yau threefold exhibits towers of superextremal BPS states in the aforementioned extreme limits as expected by the minimal WGC.