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petergreat
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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:petergreat said: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.petergreat said: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?
petergreat said: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?
CFT stands for Conformal Field Theory, which is a quantum field theory that describes the behavior of massless particles. It is a type of field theory that is invariant under conformal transformations, which preserve angles but not distances.
Active diffeomorphisms in AdS refer to the transformations that preserve the AdS metric, which is a type of spacetime metric used in the study of anti-de Sitter space. These transformations act on the coordinates of the spacetime, changing the shape of the spacetime while keeping its intrinsic properties the same.
In AdS/CFT correspondence, the bulk gravitational theory in AdS is equivalent to a boundary CFT. The active diffeomorphisms in AdS correspond to the conformal transformations in the CFT, which is known as the bulk/boundary correspondence. This provides a way to study the dynamics of the AdS space from the CFT perspective.
The isometry group of AdS is the group of transformations that preserve the AdS metric. In the CFT, this is equivalent to the conformal group, which is the group of transformations that preserve angles but not distances. This is because both the isometry group and the conformal group are related to symmetry transformations of the respective spaces.
Understanding the CFT equivalent of active diffeomorphisms in AdS allows us to gain insights into the holographic nature of AdS/CFT correspondence. It helps us understand the relationship between the bulk gravitational theory and the boundary CFT, and provides a powerful tool to study the dynamics of AdS space from a different perspective. Additionally, it has applications in various areas of theoretical physics, such as string theory and black hole physics.