Quantum gravity needs Faddeev-Popov ghosts. Feynman showed that. Take a black hole. Hawking pair production of ghost-antighost pair. One ghost falls into the hole and hits the singularity. The ghost number outside changes. Let the black hole evaporate away completely. Or even simpler, just throw a ghost into an evaporating black hole and let the black hole vanish. From no black hole initially to no black hole finally, with the global ghost number changed.
Now consider a state with no large black holes. Quantum fluctuations of the vacuum produce virtual black hole pairs. Ghosts also interact with virtual black holes. As they say, there are no global symmetries in quantum gravity. That includes total ghost number? Does this violate BRST?