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AdS/CFT as quantum to classical correspondence

by naturale
Tags: ads/cft, kaluza-klein, quantization
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naturale
#19
Feb4-13, 05:19 AM
P: 104
All your questions are discussed in Dolce's paper. Please read it.

Concerning holography try with ctrl-F and write "holography". He mentions holography 50 times.





Quote Quote by LBloom View Post
AdS/CFT dualities obey the holographic principle, but not vice versa. That is the holographic principle is an older and broader concept then AdS/CFT. AdS/CFT refers specifically to just one kind of duality where the holographic principle comes into play.
You'll see that:

"For instance, it is well known that in General Relativity (GR) the deformations of space-time associated to gravitational interaction encode the modulations of space-time periodicity of reference lengths and clocks, [44]. Moreover, [2], in this formalism the kinematical information of the particle is encoded in the geometrodynamics of the boundary in the manner of the holographic principle [45, 46]."

"a collective description of the KK modes typical of a VXD is implicit in the usual holographic description of an ordinary KK theory."

"In an ordinary XD theory, holography provides an effective and collective description of the propagation of the KK modes. However, as already noted at the end of sec.(5), by assuming a VXD, such a collective description is already explicit, even without holography. In fact the virtual KK modes naturally describe the quantum excitations of the same fundamental system (string), i.e. they are not independent fields. On the other hand, the fundamental"

read also "Comments and Outlooks" pag.40.

Holography mades the extra dimension "virtual", and virtual extra dimension is quantization.

The AdS/CFT duality is not a correspondence between abstract mathematical objects, it is a relation between a CFT in d-1 dimensions to string theory (or a theory whose origin is in ST) in d dimensions. Neither of these are well defined mathematical objects. There are QFTs that have been put on a rigorous footing by mathematicians, but for the most part this is not the case.
Now they are better defined mathematical objects.

To a certain extent there is some bad language at play. AdS/CFT has become a catchall for many different ideas and for holography in general, although it is just one subset of ideas.
I agree. This paper catches the origin of that enormous subset of ideas. The result is spectacular.
LBloom
#20
Feb4-13, 08:27 AM
P: 173
All your questions are discussed in Dolce's paper. Please read it.

Concerning holography try with ctrl-F and write "holography". He mentions holography 50 times.
I assume you're referring to blackwagonninja because I didn't have any questions about holography and was trying to explain the distinction between AdS/CFT and holography. That they are not equivalent terms. In fact I never mentioned the contents of the paper because I have not read it yet.

Please look at eq. 2.11 of Witten paper hep-th/9892150. He then writes: "The generating function of these correlation functions [quantum] would be the partition function [classical] of the conformal field theory ..." Then you can quantize as much as you want things that are already quantized, but you wont describe reality.

I don't understand why you would need to quantize. The point of AdS/CFT is that you have two quantum theories and you can simplify calculations for strong coupling if you take the classical or semiclassical limit on one side. Typically you take the semiclassical limit of a string theory to obtain a theory of supergravity, which has classical geometrical objects, but there is no need to then quantize the theory because we already know its (more) quantum origin: string theory.

If, as you say, "duality relates quantum aspects of one theory to classical aspects of another", where is the quantization? Where does QM emerge? Dolce answers to this simple question, He concludes that quantization is in the (virtual) extra dimensional formalism.
There is no quantization. Quantization refers to a process by which we construct a quantum theory out of a classical theory. Here both theories in the duality are quantum and we can recover semiclassical in the limit of weak coupling.

As I said before, I haven't read the paper in full yet, the primary purpose of my post was to explain that the ads/cft duality is much more complicated then checking symmetry groups. If and when I read the paper I would be happy to have a discussion on it.
naturale
#21
Feb6-13, 12:21 PM
P: 104
Quote Quote by LBloom View Post
There is no quantization. Quantization refers to a process by which we construct a quantum theory out of a classical theory. Here both theories in the duality are quantum and we can recover semiclassical in the limit of weak coupling.
Again, in this limit you have a correspondence between classical and quantum. AdS is used to compute quantum. Think to AdS/QCD. Witten is explicit in this "quantum phenomena such as the spontaneous breaking of the center of the gauge group, magnetic confinement, and the mass gap are coded in classical geometry." Where the quantization is in passing from classical in d dimension to quantum d-1 dimensions?

Quote Quote by LBloom View Post
As I said before, I haven't read the paper in full yet, the primary purpose of my post was to explain that the ads/cft duality is much more complicated then checking symmetry groups. If and when I read the paper I would be happy to have a discussion on it.
Let me understand. Are you saying you prefer to work with "not well defined mathematical objects" - your words? Is this because you can publish without too many complications as nobody of us will be here when N=4 super-Yang-Mills or Type IIB string theory in AdS_5 x S^5 will be tested to be wrong or correct? Are you saying that you prefer epicycles as long as people believe in that, no matter what physical reality is? If this is want you think about science, I must be twice grateful to people like Dolce and their courageous researches.These kind of black swans carry on science.

Dolce proposes a extreme reconsideration of particles nature and proves in detail a solution to longstanding issues. Every fair physicist has the duty to check whether he is correct or not.

Does it make sense to say "every particle is a clock"? Do eq.6 or eq.56 describe particles?
BandwagonNinja
#22
Feb7-13, 02:48 AM
P: 5
I am make think. Why do they no call it IIB/QFT correspondence? To me it is evident that when researches on IIB/QFT it was discovered the much bigger and more general thing AdS/CFT. But they do not call IIB/QFT so it must not be that. Pardon me for beating dead horse.
Vanadium 50
#23
Feb9-13, 09:05 AM
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