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

Mohammed Charkaoui, Rajae Sammani, El Hassan Saidi, Rachid Ahl Laamara

TL;DR

This work tests the minimal Weak Gravity Conjecture (WGC) in a 5D EFT arising from M-theory on a finite-volume Calabi–Yau threefold, focusing on the $K3×T^2$ geometry. By exploiting a fiber/base correspondence controlled by the spectral parameter $λ$, they establish a weak/strong gauge duality and construct towers of superextremal states from M2 and M5 brane wrappings on movable curves. The analysis identifies four BPS towers (two light, two heavy) that satisfy the minimal WGC in the extreme limits, and links these findings to emergent string/KK scenarios and the distance conjecture. The results provide evidence for the robustness of the minimal WGC in non-perturbative regimes and highlight dualities that could extend to broader Calabi–Yau constructions.

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.

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

TL;DR

This work tests the minimal Weak Gravity Conjecture (WGC) in a 5D EFT arising from M-theory on a finite-volume Calabi–Yau threefold, focusing on the geometry. By exploiting a fiber/base correspondence controlled by the spectral parameter , they establish a weak/strong gauge duality and construct towers of superextremal states from M2 and M5 brane wrappings on movable curves. The analysis identifies four BPS towers (two light, two heavy) that satisfy the minimal WGC in the extreme limits, and links these findings to emergent string/KK scenarios and the distance conjecture. The results provide evidence for the robustness of the minimal WGC in non-perturbative regimes and highlight dualities that could extend to broader Calabi–Yau constructions.

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.
Paper Structure (10 sections, 53 equations, 1 figure)

This paper contains 10 sections, 53 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Calabi-Yau threefolds in extreme limits
  3. Review and preliminary results
  4. Fixing the base of the fibered CYs
  5. M-theory on $K3\times T^{2}$ and the weak/strong gauge regimes
  6. Minimal WGC on $K3\times T^{2}$
  7. Refinements of the WGC
  8. The towers of the minimal WGC
  9. Conclusion and comments
  10. Appendix: 5D EFT from M-theory on $K3\times T^{2}$

Figures (1)

  • Figure 1: Two extreme configurations of the fibrations of the Calabi-Yau threefolds according to the values of the spectral parameter. They are labeled by the limits $\lambda \rightarrow \infty$ and $\lambda \rightarrow 0$.

Theorems & Definitions (1)

  • Conjecture 1