  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.
