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Is it renormalization running? Or SU(N) Gauge transformation?
This is the right answer. Bulk diffeomorphism invariance emerges along with the bulk space itself. From the conclusion of hep-th/0209104:Or nothing, because a localized diffeomorphism in the bulk doesn't affect the AdS boundary where the correspondence lives?
This emergence of diffeomorphism invariance from ‘nothing’ is analogous to what happens in the various examples of the emergence of gauge symmetries... The essential point is that gauge symmetry and diffeomorphism invariance are just redundancies of description. In the examples where they emerge, one begins with nonredundant variables and discovers that redundant variables are needed to give a local description of the long-distance physics. In [emergent] general relativity, the spacetime coordinates are themselves part of the redundant description.
I will have to think about this for a while. There are a lot of prior issues I need to understand, for example the relationship between worldsheet diffeomorphism invariance and spacetime diffeomorphism invariance, and I have to find out which of the issues are just a problem for me and my incomplete understanding, and which are unsolved problems even for the experts! Meanwhile, there are no dilatons in these papers, but arXiV:0805.2203 and "staff.science.uva.nl/~jdeboer/publications/francqui.pdf"[/URL] look at some of the space-time diffeo issues.Something else comes to mind. The dilaton inherent in string theory, and therefore AdS/CFT, breaks the equivalence principle. Does this mean diffeomorphism invariance is also broken? In other words, is it possible to have a diffeomorphism invariant theory which violates the equivalence principle?
As I understand:Something else comes to mind. The dilaton inherent in string theory, and therefore AdS/CFT, breaks the equivalence principle. Does this mean diffeomorphism invariance is also broken? In other words, is it possible to have a diffeomorphism invariant theory which violates the equivalence principle?