Analogy for the AdS/CFT Correspondence

Question

Some time ago, I heard about a simple analogy for the AdS/CFT correspondence to something in everyday life. Consider a room filled with furniture, with the walls of the room covered in mirrors. The 2D mirrors we can think of as an N-dimensional CFT--the furniture is the corresponding entities in the N+1-dimensional AdS.

I feel like this is an over-simplification. What is lost in the actual AdS/CFT correspondence in this analogy? I feel like information in the 3D world is lost in the 2D mirror--is this true in the AdS/CFT correspondence? That is, is there information in the AdS that can't be expressed in the CFT?

This post imported from StackExchange Physics at 2015-06-05 09:23 (UTC), posted by SE-user Joshuah Heath

Comments

The mirror won't tell you everything about the room. It can't tell you distances between objects, for example, and you will lose information if one object obstructs the view of another object. AdS/CFT is an exact equivalence. Knowing all observables in the boundary CFT lets you construct any observable in the bulk theory.

This post imported from StackExchange Physics at 2015-06-05 09:23 (UTC), posted by SE-user Andrew

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Where did you hear about this? Is this analogy accurate ?

This post imported from StackExchange Physics at 2015-06-05 09:23 (UTC), posted by SE-user Prathyush

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@Prathyush I don't remember exactly where--like I said in the post, it was quite some time ago. I think it was in some popular science magazine, and thus I was (and still am) somewhat skeptical about the accuracy of such an analogy. Nevertheless, it does raise the question of whether or not there is anything lost when going to the AdS, but if Andrew is right, then the AdS/CFT correspondence is an "exact equivalence", and thus nothing appears to be lost.

This post imported from StackExchange Physics at 2015-06-05 09:23 (UTC), posted by SE-user Joshuah Heath

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@JoshuahHeath, I just want to know if any aspect of this analogy is even remotely correct.

This post imported from StackExchange Physics at 2015-06-05 09:23 (UTC), posted by SE-user Prathyush

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@Andrew - just a thought about the accuracy of the analogy. Can't you tell the distance between objects by using the fact that there are two images (one on each side of the room)? To do this you'd need to know the size of the room, but this is encoded in the boundary data. This seems like a nice property of the analogy since then boundary data at separated points is encoded by passage through the bulk... It would be interesting to hear people's take on this!

This post imported from StackExchange Physics at 2015-06-05 09:23 (UTC), posted by SE-user Edward Hughes

Answer 1

The analogy is not perfect. In principle the AdS/CFT correspondence is exact, however the mirror analogy is not. It is well known in psychophysics that recovering the structure of a scene from a 2d image is an ill posed problem. There are may heuristics you can use to recover the shape and depth of objects based only on the projected image, and these usually give accurate enough results, but there is an infinite number of solutions, all compatible with the same image.

This post imported from StackExchange Physics at 2015-06-05 09:23 (UTC), posted by SE-user bruce smitherson

Comments

Is there anything about analogy that is actually correct?

This post imported from StackExchange Physics at 2015-06-05 09:23 (UTC), posted by SE-user Prathyush