The Weak Gravity Conjecture, RG Flows, and Supersymmetry

TL;DR

This paper investigates one-loop divergences in Einstein-Maxwell and supergravity theories, demonstrating how they influence the weak gravity conjecture and black hole stability, with supersymmetry providing protection against quantum corrections.

Contribution

It shows that one-loop divergences lead to positivity of higher-derivative corrections, supporting the weak gravity conjecture, and reveals supersymmetry's role in stabilizing black holes against quantum effects.

Findings

Positivity of higher-derivative corrections supports the weak gravity conjecture.

Charged extremal black holes can decay into smaller ones, satisfying the conjecture.

Supersymmetry protects dyonic black holes from quantum corrections, ensuring their stability.

Abstract

We study one-loop divergences in Einstein-Maxwell theory and their implications for the weak gravity conjecture. In particular, we show that renormalization of these divergences leads to positivity of higher-derivative corrections to the charge-to-mass ratio of dyonic black holes. This allows charged extremal black holes to decay into smaller ones, and so the weak gravity conjecture is automatically satisfied. We also extend this analysis to a much wider class of Einstein-Maxwell theories coupled to additional massless matter fields and find the same result. We then go on to study one-loop divergences in $\mathcal{N} \geq 2$ supergravity and show that dyonic black holes in these theories are protected against one-loop quantum corrections, even if the black hole breaks supersymmetry. In particular, extremal dyonic black holes are stabilized by supersymmetry and cannot decay.