Minimal Weak Gravity Conjecture And Gauge Duality in M-theory on K3xT2

TL;DR

This paper explores how M-theory compactified on specific Calabi-Yau threefolds supports the minimal Weak Gravity Conjecture by demonstrating towers of superextremal BPS states in both weak and strong coupling regimes, linking geometric structures to physical predictions.

Contribution

It establishes a geometric correspondence in Calabi-Yau threefolds that connects weak and strong gauge couplings, providing a non-perturbative probe of the minimal WGC in M-theory.

Findings

Demonstrates towers of superextremal BPS states in extreme coupling limits.

Establishes a geometric relation between fiber and base curves in Calabi-Yau threefolds.

Supports the minimal WGC through non-perturbative analysis.

Abstract

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.