When I was editing the Physics.SE tag wiki for ads-cft, I initially wrote something on the lines of :
The AdS/CFT correspondence is a special case of the holographic principle. It states that a gravitating theory in Anti-de-Sitter (AdS) space is exactly equivalent to the gauge theory/Conformal Field Theory (CFT) on its boundary.
Then I thought, "Wait, it can't be ANY gravitating theory, right? It must be a theory of Quantum Gravity, right?". So I changed it to:
The AdS/CFT correspondence is a special case of the holographic
principle. It states that a quantum gravitating theory in
Anti-de-Sitter (AdS) space is exactly equivalent to the gauge
theory/Conformal Field Theory (CFT) on its boundary.
Now, I'm a bit unsure. Can AdS/CFT work for classical gravity theories? .
I have seen the questions Which CFTs have AdS/CFT duals? and What is on the AdS side in AdS/CFT supergravity or string theory?, but my question is a bit different.. It is a special case of the opposite of the first question, and is more general than the second. From Lubos Motl's answer to the second question, I see that supergravity theories don't form AdS theories with CFT duals, but is that true for all classical theories?.
And a bit more general question: If the answer to the above question^ is yes, then do all gravitational theories in AdS's have CFT duals? . This is pretty much the opposite of Which CFTs have AdS/CFT duals?.
For example, is General Relativity such a theory; with a CFT dual? If so, what would be it's CFT dual? What about... Nope I'm not going to ask about Newtonian Gravity, or Aristotilean Gravity, for obvious reasons. And certainly not LQG (something that doesn't respect holography in the most trivial situations, couldn't here.).
This post imported from StackExchange Physics at 2014-03-07 16:31 (UCT), posted by SE-user Dimensio1n0