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"Dictionary" between QFTs in D and D-1 dimensions?

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Considering Einstein equations, suppose, for instance, that the RHS, the stress-energy tensor, is uniquely due to the electromagnetic field. Now, if we imagine a quantized version of these Einstein equations, we have a quantum field theory in $D$ dimensions (here the quantum electromagnetic field) as "source" of a "quantum gravity" theory in $D$ dimensions, so we may consider these equations as a kind of "dictionary" between these two theories.

On an other way, there are some holographic dualities, which relates some quantum theory of gravity in a $D$ dimensional space with boundary, with some quantum field theory on the boundary ( $D-1$ dimensions)

So, the question is, if, "skipping gravity", it is possible or not, and how, to directly relate the QFT in $D$ dimensions (source of gravity), and the other QFT (on the boundary) in $D-1$ dimensions.

This post imported from StackExchange Physics at 2014-08-02 11:04 (UCT), posted by SE-user Trimok

asked Aug 2, 2014 in Theoretical Physics by Trimok (955 points) [ revision history ]
edited Aug 2, 2014 by Arnold Neumaier

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