Higher-Group Symmetries and Weak Gravity Conjecture Mixing

Abstract

In four-dimensional axion electrodynamics, a Chern-Simons coupling of the form θF ∧ F leads to a higher-group global symmetry between background gauge fields. At the same time, such a Chern-Simons coupling leads to a mixing between the Weak Gravity Conjectures for the axion and the gauge field, so that the charged excitations of a Weak Gravity Conjecture-satisfying axion string will also satisfy the Weak Gravity Conjecture for the gauge field. In this paper, we argue that these higher-group symmetries and this phenomenon of Weak Gravity Conjecture mixing are related to one another. We show that this relationship extends to supergravities in 5, 6, 7, 8, 9, and 10 dimensions, so higher-dimensional supergravity is endowed with precisely the structure needed to ensure consistency with emergent higher-group symmetries and with the Weak Gravity Conjecture. We further argue that a similar mixing of Weak Gravity Conjectures can occur in two-term Chern-Simons theories or in theories with kinetic mixing, though the connection with higher-group symmetries here is more tenuous, and accordingly the constraints on effective field theory are not as sharp.

Generalized Symmetry Breaking Scales and Weak Gravity Conjectures

“…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].…”

Some open questions in axion theory

“…The Weak Gravity Conjecture places a bound on the tension of an axion string of the form T ≤ c ′ f a M Pl , but once again the precise value of the coefficient c ′ remains an important open question [197] with applications to black hole physics [198,199]. In theories with aF F couplings, the excitations of the axion string will satisfy the Weak Gravity Conjecture for the gauge field provided the axion string satisfies its version of the Weak Gravity Conjecture, leading to a mixing between of different versions of the Weak Gravity Conjectures [200,201] which mirrors the mixing of background gauge fields into a higher-group symmetry [202]. These calculations generally lack precise order-one coefficients, however, so an improved understanding of axion strings could lead to a sharpening of the Weak Gravity Conjecture and more precise constraints for quantum gravity on low-energy effective field theory.…”