Wednesday, 22 October 2014

string theory - 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?



Answer



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.


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