# Global symmetries in quantum gravity

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?

• For example, one may explain why the black holes destroy the non-gauged baryon number. Take a star with $B=10^{48}$, make it collapse into a black hole. Long-distance approximation - GR - will show that the black hole event horizon is locally independent of the baryon charge because there are no fields that could remember the baryon charge. So the Hawking radiation from the event horizon, by locality, has to be independent of the initial baryon charge, too. It follows that the black hole emits radiation that is independent of the initial $B$, which means $B=0$ radiation in average: B is gone. – Luboš Motl Feb 10 '11 at 11:44
• @Lubos: I'm a bit puzzled by this. How do you know that you can trust a semiclassical calculation all the way to the end of the black hole evaporation? Wouldn't it be possible that in a truly quantum gravity description the black hole actually "knows" that it contains some nonzero $B$ and that at the end of evaporation you get it back? – bangnab Feb 18 '11 at 8:52
• @inovaovao: Because there isn't enough mass at the end of evaporation to get $10^{48}$ baryons back. – Ron Maimon Jul 27 '12 at 6:46