Weak Gravity Conjecture from Unitarity and Causality

TL;DR

This paper demonstrates that unitarity and causality constraints imply the existence of charged extremal black holes as the required states in the weak gravity conjecture across various theories, including string theory scenarios.

Contribution

It provides a novel proof of the weak gravity conjecture by linking black hole properties to unitarity and causality constraints in a broad class of theories.

Findings

Heavy extremal black holes can serve as the charged states required by the weak gravity conjecture.

The argument applies to theories with light neutral bosons and different Regge state configurations.

The result supports the conjecture's validity in string theory and related UV completions.

Abstract

The weak gravity conjecture states that quantum gravity theories have to contain a charged state with a charge-to-mass ratio bigger than unity. By studying unitarity and causality constraints on higher derivative corrections to the charge-to-mass ratio of extremal back holes, we demonstrate that heavy extremal black holes can play the role of the required charged state under several assumptions. In particular, our argument is applicable when the higher spin states Reggeizing graviton exchange are subdominant in the photon scattering. It covers (1) theories with light neutral bosons such as dilaton and moduli, and (2) UV completion where the photon and the graviton are accompanied by different sets of Regge states just like open string theory. Our result provides an existence proof of the weak gravity conjecture in a wide class of theories, including generic string theory setups with the dilaton or other moduli stabilized below the string scale.