  There are strong reasons to believe that global symmetries of quantum
theories cannot be exact in the presence of gravity. While this has been argued
at the qualitative level, establishing a quantitative statement is more
challenging. In this work we take new steps towards quantifying symmetry
violation in EFTs with gravity. First, we evaluate global charge violation by
microscopic black holes present in a thermal system, which represents an
irreducible, universal effect at finite temperature. Second, based on general
QFT considerations, we propose that local symmetry-violating processes should
be faster than black hole-induced processes at any sub-Planckian temperature.
Such a proposal can be seen as part of the "swampland" program to constrain
EFTs emerging from quantum gravity. Considering an EFT perspective, we
formulate a conjecture which requires the existence of operators violating
global symmetry and places quantitative bounds on them. We study the interplay
of our conjecture with emergent symmetries in QFT. In models where gauged
U(1)'s enforce accidental symmetries, we find that constraints from the Weak
Gravity Conjecture can ensure that our conjecture is satisfied. We also study
the consistency of the conjecture with QFT models of emergent symmetries such
as extradimensional localization, the Froggatt-Nielsen mechanism, and the
clockwork mechanism.
