Generalized Symmetry Breaking Scales and Weak Gravity Conjectures

TL;DR

By positing that generalized global symmetries are badly broken at or below the Planck scale, the paper provides a unified symmetry-based framing for key quantum gravity conjectures. It derives the Weak Gravity Conjecture and magnetic WGC from electric and magnetic 1-form symmetry breaking via light charged towers and via KK reductions, and extends the logic to non-Abelian, axion, and distance conjectures. It also shows that shift-symmetry breaking of moduli and axions naturally leads to the distance conjecture and axion WGC, with KK viewpoints linking 4D and higher-dimensional pictures. The resulting perspective ties swampland conditions to the emergence of charged towers and the absence of global symmetries, and outlines directions for refining the framework and extending to discrete/higher-form cases.

Abstract

We explore the notion of approximate global symmetries in quantum field theory and quantum gravity. We show that a variety of conjectures about quantum gravity, including the weak gravity conjecture, the distance conjecture, and the magnetic and axion versions of the weak gravity conjecture can be motivated by the assumption that generalized global symmetries should be strongly broken within the context of low-energy effective field theory, i.e. at a characteristic scale less than the Planck scale where quantum gravity effects become important. For example, the assumption that the electric one-form symmetry of Maxwell theory should be strongly broken below the Planck scale implies the weak gravity conjecture. Similarly, the violation of generalized non-invertible symmetries is closely tied to analogs of this conjecture for non-abelian gauge theory. This reasoning enables us to unify these conjectures with the absence of global symmetries in quantum gravity.

Figures (1)

• Figure 1: The action of a $p$-form symmetry operator $U_\alpha$ on a $p$-dimensional extended operator $V( \mathcal{C}^{(p)} )$. When $U_\alpha$ surrounds $\mathcal{C}^{(p)}$, it acts by a phase $\exp ({i \alpha q })$.