Towards a Swampland Global Symmetry Conjecture using Weak Gravity

Understand

It is widely believed and in part established that exact global symmetries are inconsistent with quantum gravity.

• One then expects that approximate global symmetries can be quantitatively constrained by quantum gravity or swampland arguments.
• We provide such a bound for an important class of global symmetries: Those arising from a gauged $U(1)$ with the vector made massive via Higgsing with an axion.
• The latter necessarily couples to instantons, and their action can be constrained, using both the electric and magnetic version of the axionic weak gravity conjecture, in terms of the cutoff of the theory.