The Weak Gravity Conjecture and Axion Strings

TL;DR

This paper explores the implications of the Weak Gravity Conjecture for axion strings, suggesting that gauge theories with axions typically involve stringy towers of charged states, with exceptions like Kaluza-Klein theories.

Contribution

It provides a bottom-up argument linking the WGC to the existence of axion strings and discusses conditions under which high-spin states are delayed or absent.

Findings

Axion strings carry charged modes from anomaly inflow.

Kaluza-Klein theories evade the string tower conclusion.

Arguments support the Emergent String and Distant Axionic String Conjectures.

Abstract

Strong (sublattice or tower) formulations of the Weak Gravity Conjecture (WGC) imply that, if a weakly coupled gauge theory exists, a tower of charged particles drives the theory to strong coupling at an ultraviolet scale well below the Planck scale. This tower can consist of low-spin states, as in Kaluza-Klein theory, or high-spin states, as with weakly-coupled strings. We provide a suggestive bottom-up argument based on the mild $p$-form WGC that, for any gauge theory coupled to a fundamental axion through a $\theta F \wedge F$ term, the tower is a stringy one. The charge-carrying string states at or below the WGC scale $g M_\mathrm{Pl}$ are simply axion strings for $\theta$, with charged modes arising from anomaly inflow. Kaluza-Klein theories evade this conclusion and postpone the appearance of high-spin states to higher energies because they lack a $\theta F \wedge F$ term. For abelian Kaluza-Klein theories, modified arguments based on additional abelian groups that interact with the Kaluza-Klein gauge group sometimes pinpoint a mass scale for charged strings. These arguments reinforce the Emergent String and Distant Axionic String Conjectures. We emphasize the unproven assumptions and weak points of the arguments, which provide interesting targets for further work. In particular, a sharp characterization of when gauge fields admit $\theta F \wedge F$ couplings and when they do not would be immensely useful for particle phenomenology and for clarifying the implications of the Weak Gravity Conjecture.