The Weak Gravity Conjecture and axion strings

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 θF ∧ F term, the tower is a stringy one. The charge-carrying string states at or below the WGC scale gMPl are simply axion strings for θ, 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 θF ∧ 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 θF ∧ F couplings and when they do not would be immensely useful for particle phenomenology and for clarifying the implications of the Weak Gravity Conjecture.

Generalized Symmetry Breaking Scales and Weak Gravity Conjectures

“…This ultraviolet renormalization of the Yang-Mills coupling is driven by a tower of charged particles which drive the gauge sector to strong coupling. Here we see that this tower of charged particles plays a key role in breaking the axion shift symmetry, similar to the recent analysis of [79].…”

“…For instance, we have not examined the weak gravity conjecture for p-form gauge fields with p > 1, which lead to p-form electric symmetries and (d − p − 2)form magnetic symmetries that must be broken by charged (p − 1)-branes and (d − p − 3)branes, respectively. Relatedly, we have not considered the topic of higher-group symmetries [56,75,80,83,[88][89][90][91], which lead to mixing of weak gravity conjectures between p-form gauge fields of different degrees [79,92]. Similarly, we have not delved into the breaking of so-called "(−1)-form symmetries" [80,[93][94][95], which are related to the absence of free parameters in quantum gravity and the absence of nontrivial cobordism groups [96,97].…”

“…As discussed in [79], gauge theories with axions can be usefully distinguished by whether or not the gauge field couples to the axion via a φTr (F ∧ F ) coupling. If such a coupling exists, then the electric and magnetic symmetries of the axion and the gauge field are tied up in a higher-group structure [80][81][82][83], and the excitations of the axion string carry charge under the gauge field [84].…”

“…In fact, Kaluza-Klein theory may be the only such example, as the work of[79,85,86] suggests that the weak coupling limit of a gauge field with a θF ∧ F coupling is a tensionless string limit, and a weak coupling limit without such a coupling is a decompactification limit.…”

The Weak Gravity Conjecture: A Review

“…As a final qualitative check, we review an argument for the WGC in the presence of Chern-Simons terms [137]. This argument is somewhat circular from the point of view of establishing the WGC, as it assumes the WGC for axions and charged strings in order to prove the ordinary WGC for charged particles.…”