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.
Highlights
Introduction.—One of the greatest appeals of string theory is that it provides a consistent framework for constructing a variety of models for particle physics and cosmology while incorporating quantum gravity
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
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
Summary
The weak gravity conjecture states that quantum gravity theories have to contain a charged state with a charge-to-mass ratio bigger than unity. 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. (2) UV completion where the photon and the graviton are accompanied by different sets of Regge states (just like open string theory), and those associated to the graviton are subdominant in the photon scattering These two classes cover a wide variety of theories, including generic stringy setups, providing a strong evidence of the mild form of WGC. We focus on the D 1⁄4 4 case in this Letter, and relegate the extension to general spacetime dimension D ≥ 5 to the Supplemental Material [22], which includes Refs. [23,24,25,26,27,28,29,30,31,32]
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