A Tower Weak Gravity Conjecture from Infrared Consistency

TL;DR

This paper derives infrared consistency conditions in 3D and 4D effective field theories with charged particles, leading to a tower version of the weak gravity conjecture that includes bifundamentals and bounds on charge-to-mass ratios.

Contribution

It establishes a new connection between infrared consistency, causality, and the weak gravity conjecture, including a tower version and implications for Kaluza-Klein compactifications.

Findings

Theories must contain bifundamentals and satisfy the convex-hull condition.

Charge-to-mass ratios of an infinite tower of particles are bounded from below.

The tower includes bifundamentals but does not necessarily occupy a charge lattice.

Abstract

We analyze infrared consistency conditions of 3D and 4D effective field theories with massive scalars or fermions charged under multiple $U(1)$ gauge fields. At low energies, one can integrate out the massive particles and thus obtain a one-loop effective action for the gauge fields. In the regime where charge-independent contributions to higher-derivative terms in the action are sufficiently small, it is then possible to derive constraints on the charge-to-mass ratios of the massive particles from requiring that photons propagate causally and have an analytic S-matrix. We thus find that the theories need to contain bifundamentals and satisfy a version of the weak gravity conjecture known as the convex-hull condition. Demanding self-consistency of the constraints under Kaluza-Klein compactification, we furthermore show that, for scalars, they imply a stronger version of the weak gravity conjecture in which the charge-to-mass ratios of an infinite tower of particles are bounded from below. We find that the tower must again include bifundamentals but does not necessarily have to occupy a charge (sub-)lattice.