Global symmetries in quantum gravity

Question

In several papers (including a recent one by Banks and Seiberg) people mention a "folk-theorem" about the impossibility to have global symmetries in a consistent theory of quantum gravity. I remember having heard one particular argument that seemed quite reasonable (and almost obvious), but I can't remember it.

I have found other arguments in the literature, including (forgive my sloppiness):

• In string theory global symmetries on the world-sheet become gauge symmetries in the target space, so there is no (known) way to have global symmetries.

• in AdS/CFT global symmetries on the boundary correspond to gauge symmetries in the bulk so there again there is no way to have global symmetries in the bulk.

• The argument in the Banks-Seiberg paper about the formation of a black hole charged under the global symmetry.

I find none of these completely satisfactory. Does anybody know of better arguments?

Answer 1

Perhaps this is just rephrasing your last explanation, so I am not sure if you consider this as a "better argument", but I'll give you a good reference for further reading.

Quantum gravity may break global symmetries because the global charge can be eaten by virtual black holes or wormholes, see this paper.

Answer 2

If one builds a QG in a flat space-time, a la Logunov's RTG, then one may have global symmetries. But it is forbidden to say and is punished, beware.