Infrared Consistency and the Weak Gravity Conjecture

TL;DR

This paper investigates the weak gravity conjecture through low-energy effective field theory, deriving infrared consistency conditions that relate charge-to-mass ratios and higher-dimension operators to ensure physical consistency.

Contribution

It provides a novel infrared perspective on the weak gravity conjecture by deriving bounds from analyticity, unitarity, and causality constraints in effective field theories.

Findings

Bound on charge-to-mass ratio $q/m$ for small $eta$

Infrared consistency conditions constrain effective action parameters

Analysis extended from three to four spacetime dimensions

Abstract

The weak gravity conjecture (WGC) asserts that an Abelian gauge theory coupled to gravity is inconsistent unless it contains a particle of charge $q$ and mass $m$ such that $q \geq m/m_{\rm Pl}$. This criterion is obeyed by all known ultraviolet completions and is needed to evade pathologies from stable black hole remnants. In this paper, we explore the WGC from the perspective of low-energy effective field theory. Below the charged particle threshold, the effective action describes a photon and graviton interacting via higher-dimension operators. We derive infrared consistency conditions on the parameters of the effective action using i) analyticity of light-by-light scattering, ii) unitarity of the dynamics of an arbitrary ultraviolet completion, and iii) absence of superluminality and causality violation in certain non-trivial backgrounds. For convenience, we begin our analysis in three spacetime dimensions, where gravity is non-dynamical but has a physical effect on photon-photon interactions. We then consider four dimensions, where propagating gravity substantially complicates all of our arguments, but bounds can still be derived. Operators in the effective action arise from two types of diagrams: those that involve electromagnetic interactions (parameterized by a charge-to-mass ratio $q/m$) and those that do not (parameterized by a coefficient $\gamma$). Infrared consistency implies that $q/m$ is bounded from below for small $\gamma$.