Infrared Consistency and the Weak Gravity Conjecture

TL;DR

The paper investigates the weak gravity conjecture (WGC) from the standpoint of low-energy infrared effective field theory, asking whether violations of the WGC would trigger infrared pathologies. By analyzing photon–graviton EFTs in three and four spacetime dimensions, Cheung and Remmen derive infrared consistency conditions from analyticity of light-by-light scattering, unitarity of any UV completion, and causality in nontrivial backgrounds. In 3D they obtain a simple bound a' ≥ 0 and show that, for small purely gravitational corrections γ, the charge-to-mass ratio must satisfy z ≥ 1, a 3D analog of the WGC; in 4D they derive unitarity and causality bounds a1' ≥ 0, a2' ≥ 0, and a1' + a2' ≥ 0, with the small-γ regime giving z ≥ 2 for both fermions and scalars. Together, these results connect infrared consistency to the WGC and highlight how gravity constrains low-energy couplings, offering a path to derive swampland criteria from IR data and informing UV completion expectations.

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 $γ$). Infrared consistency implies that $q/m$ is bounded from below for small $γ$.

Figures (5)

• Figure 1: Diagrams involving photons (single wavy), gravitons (double wavy), and charged matter (solid) that contribute to light-by-light scattering, organized in terms of scaling with $z=q/m$, as defined in Eq. (\ref{['eq:gamma']}). Here, $\gamma$ parameterizes purely gravitational corrections.
• Figure 2: Setup for the construction of a CCC in 3D, using superluminal photons in a theory that violates Eq. (\ref{['eq:consistency3d']}). The construction, illustrated here in a constant-time slice of the two spatial dimensions, consists of two circular bubbles of thermal radiation, each of radius $\ell$ and separation $L\gg\ell$, with relative speed $u<1$ (green arrow). Signals (red dashed arrows) sent back and forth would be superluminal within the bubbles, creating a CCC for large $u$.
• Figure 3: Bounds on the 4D photon-graviton effective theory derived from integrating out a fermion (left) or scalar (right) and expressed in terms of the contributions coming from electromagnetism (parameterized by $z=q/m$) and pure gravity (parameterized by $\gamma$). The cross-hatched regions are forbidden by arguments from unitarity, which apply to $\gamma =\gamma_1$ ( red $\boxslash$) and $\gamma=\gamma_2$ ( blue $\boxbslash$), and arguments from analyticity and superluminality, which both apply to $\gamma= \gamma_1+\gamma_2$ ( green $\boxbar$). The WGC forbids $z<1$, which overlaps with much of the region also forbidden by infrared consistency.
• Figure 4: Conformal diagram for a maximally-extended Schwarzschild black hole. The effective horizon (dotted black) shrinks in a theory failing our superluminality bound. Superluminal photon propagation (red dashed arrow) allows observers in regions I and III to communicate.
• Figure 5: Conformal diagram (left) and embedding diagram of a spacelike slice (right) of the maximally-extended Schwarzschild black hole, describing wormhole mouths in relative motion. In a theory with superluminal propagation, the effective horizon (dotted black) shrinks and the wormhole becomes traversable by a signal sent from region III to I (red dashed arrow). The codimension-one surfaces (dashed green) at large spatial distance from the mouths are identified, albeit boosted relative to one another (green arrows). Also shown is a particular tangent codimension-three spacelike surface (dashed blue).