There are various models in physics based on the famous holographic principle (https://en.wikipedia.org/wiki/Holographic_principle)

This does not always work since in these models we must find a correlation between two theories, one in $n$ Dimensions and the other one in $n-1$ Dimensions, and such correlation does not always exist.

However, there is an "alternative" in holographic models, called "holographic screens" (https://arxiv.org/abs/hep-th/9906022) which eliminates the need of having a boundary in these models. This makes me think that we can represent any theory or model in $n$ Dimensions without the necessity of finding a correlation to a $n-1$ Dimensional theory or model, but I would like to confirm it.

So, in summary, can we use Holographic Screens to make a "1 to 1" representation of a theory or model? I mean, can we use Holographic Screens to represent the same theory or model without changing nothing of it (without changing it dimensions or any of its properties)?

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    $\begingroup$ For a generic holographic screen we have no idea what kind of theory would be living on it. This is discussed in section 4.2 of Bousso's paper. In particular, for screens with areas changing with time the number of dof is not constant. $\endgroup$ – A.V.S. Jul 29 at 7:50
  • $\begingroup$ @A.V.S. What do you exactly mean with this? What do you want to say with "For a generic holographic screen we have no idea what kind of theory would be living on it". Also, what about holographic screens with a fixed number of degrees of freedom? $\endgroup$ – user235953 Jul 31 at 2:07
  • $\begingroup$ What I mean is that a few examples where we have any idea about the theory on the screen/boundary come from knowing the symmetry group acting on it. This group could be used to bootstrap (as in conformal bootstrap) the theory. For a generic spacetime the screen may not have any symmetries at all. $\endgroup$ – A.V.S. Jul 31 at 6:27
  • $\begingroup$ @A.V.S. There is another article written by Bousso that could be what you are referring to: arxiv.org/pdf/hep-th/0203101.pdf. There he wrote (section IX): "In more general spacetimes, it remains unclear how the holographic principle can be made manifest through a theory with explicitly holographic degrees of freedom. In particular, one can argue that the screen should not be presumed; all information about the geometry should come out of the theory itself." $\endgroup$ – user235953 Aug 3 at 1:34
  • $\begingroup$ @A.V.S. If I understood this right (I'm not sure if I did) this means that there are situations where we cannot know how can we represent the theory in the bulk on the screen using the "classical" holographic principle and explicitly using holographic-principle degrees of freedom. But we could argue that the theory itself would give that information (Maybe the theory would not be encoded according to the "classical" holographic principle, but according to other "kind" of holographic principle. For example, one which does not follow/respect the Bekenstein bound)... But is this right? $\endgroup$ – user235953 Aug 3 at 1:34

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