Is AdS/CFT geometric or quantum?

[Michael77]

Hi everyone, long time lurker first time poster. There's been a some debate here on AdS/CFT and I can't resolve the facts of the matter. I have read Maldacena's large-N paper but of course there is no mention of AdS/CFT in there. The reason I'm posting is because I was hoping someone could share a peer-reviewed paper which clears this up instead of just sharing an opinion. Are there any AdS/CFT topical review papers that anyone knows?

 

[atyy]

When N is large, the bulk is very close to classical gravity which is spacetime geometry.

http://arxiv.org/abs/0909.0518

"(a) Some ordinary quantum field theories (QFTs) are secretly quantum theories of gravity.
(b) Sometimes the gravity theory is classical, and therefore we can use it to compute interesting observables of the QFT."

http://arxiv.org/abs/1010.6134

"The equality means a one-to-one mapping of the spectra, at any given value of the energy and other quantum numbers. It also includes equality of observables, namely the correlation functions of operators with an appropriate dictionary between the two sides."

"It is sometimes asserted that the evidence supports only a weak form of the duality, but it is not clear what a sensible weak form would be. Suggestions include ...

Thus, by far the simplest way to account for all the facts is that the duality is an exact statement. Of course, we only have an explicit construction of the theory on the QFT side, so I mean that the QFT must agree with all of the approximations we have to the string theory, and with any future constructions of the theory. Anyway, the QFT is fully quantum mechanical and consistent, and as we have noted it includes all the graviton states (with the right trilinear interactions), so at the very least it is some theory of quantum gravity."

 

[Michael77]

Thanks, I have seen that McGreevy paper but I didn't read it. Both of these papers look helpful, thanks a lot. Can you please help clear one other thing for me? When I try to read these papers I am often confused by D, d and N. What is the convention for these variables?

 

[atyy]

The large N is the size of a matrix (eg. http://arxiv.org/abs/0909.0518 p14). There is another $\mathcal{N}$ that is used to describe a property of a particular supersymmetric QFT as in $\mathcal{N}=4$ (eg. http://arxiv.org/abs/0909.0518 p54). I think D and d are usually used to refer to the spacetime dimension. But notation can vary, since it's just a matter of convention.