In holographic theories about the universe, the one being in the boundary of the space, takes information of the higher dimensional universe, so, two different theories can describe the two universes. If the lower dimensional universe gathers information about the higher one, couldn't exist also the possibility that this universe would be described, not by a different but equivalent theory than that describing the higher one, but by the same exact theories of the higher one?
Can this "holographic duality" between theories (as it is the case for AdS/CFT), be true for whatever two theories? If not, then what does establish what theories can be dual?
https://en.wikipedia.org/wiki/AdS/CFT_correspondence
https://en.wikipedia.org/wiki/Holographic_principle
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