Talk:AdS/CFT correspondence

Too much popular
This article is so popular it is unreadable. A good article should contain mathematics first, then its description or interpretation in words, both in technical terms and in "layman" terms for beginners. Describing AdS as "imagine you have a stsck pf hyperbolic planes..." is sht, the correct way would be to provide the AdS metric and explain that it desceibes hyperbolaes and marhematically show why. The approach of this article is backwards and wrong and good for mothing because in later terms makes it unreadable and the issue incomperhensible and free for individual interpretation, which the issue is the exact opposite - it is mathematics concept and mathematics is exact. — Preceding unsigned comment added by 151.236.226.176 (talk) 17:24, 19 May 2017 (UTC)

Comments
It's not a "conceptual breakthrough" if it's unproven. Making the conjecture showed fine insight, and it is clear that valuable results will flow from verifying its status. If it's true then the QCD particle spectrum can be analysed using perturbation theory; if it's false then the explanation, juxtaposed with the fact that it often works, will tell us something interesting. But to build on conjectures is risky, and effort is better spent on checking whether it's true. - AG, Stockport, UK.

I have two questions: Thanks, AxelBoldt (talk) 15:52, 9 April 2009 (UTC)
 * Have any instances of the correspondence been proven?
 * In the correspondence between AdS5&times;S5 and N=4 Yang-Mills theory on the conformal boundary, is our real universe supposed to be the former or the latter? In other words, are we living in the higher dimensional space whose image is the hologram, or in the hologram itself?
 * No, nothing proven.
 * If there is a correspondence, it means they are identical and it doesn't matter which one the universe is. In this particular case our universe is neither as there is no $$\mathcal N=4$$ supersymmetry or conformality realized in reality.
 * MuDavid (talk) 15:10, 17 March 2010 (UTC)


 * Comment: it's still a breakthrough. Also, the mathematical correspondence is being applied in condensed matter physics a lot right now. Someone should include that in the article. Also, given the importance of this topic, I would like to see an introduction for lay-readers, (if that is even possible) or something for those who are not gods of theoretical physics (such as myself). Danski14(talk) 22:24, 8 September 2010 (UTC)

The article need to expand with a section about Holographic Superconductors. —Preceding unsigned comment added by 79.145.145.119 (talk) 04:22, 30 April 2011 (UTC) ?

wtf? totaly unreadable, even for somebody who understands the basics of concepts such as quantum stats, quantum entanglement, many world theory and such... this was totaly unreadable. — Preceding unsigned comment added by 85.226.1.123 (talk) 08:04, 5 January 2012 (UTC)

Can Someone Explain Why This Is Important?
I agree with the above. If you know what this is telling you, you might be able to understand it. But the purpose of an encyclopedia is to explain the topic to people who do not already know about it.

I was directed to this article from the philosophy of time entry. I have a good layman's understanding of quantum theory and string theory, but what this means, why it's important, and what its implications are do not appear to be available in this article. Can we have it interpreted for the rest of us?

64.134.45.58 (talk)


 * Important because it shows how far in the weeds modern physics is with its substitution of mathematics for real things in nature. The crowning glory is nothing with properties (general relativity) and a real existent without extent (strings). Only the overall backwardness of human culture could bring such a thing about, an excellent example of how the 98% steer, govern, and culturally determine the 2%. So important in a nude emperor kind of way (besides the fun maths). 198.255.198.157 (talk) 20:58, 8 December 2013 (UTC)

Picture?
Could someone help me find a free picture for the section on the quark-gluon plasma? I'm thinking something like this would be good:

http://cdn.zmescience.com/wp-content/uploads/2011/05/quark-gluon-plasma2.jpg

Thanks. Polytope24 (talk) 03:16, 22 August 2013 (UTC)

A welcome effort... a few comments
I'm glad to see this kind of serious content being presented here! As a non-physicist trying to make sense of this I should, however, make some comments...


 * The purpose of the anti-de Sitter space needs to be clarified a bit. I'm assuming that the point of the pretty picture is that it represents a space with 450 degrees in every circle (three 90-degree angles and three 60-degree angles).  I assume this is just a conceptual diagram?  We have an open universe but not a noticeable increased number of degrees in a circle, and the way the diagram looks that is true for every point in the space, so our diagram would look almost but not exactly quite like a checkerboard?  Or is this a matter of scale???


 * "hyperbolic space can have more than two dimensions and one can "stack up" copies of hyperbolic space to get higher dimensional models of anti-de Sitter space." -- this is beside an image of a cylindrical prism of anti-de Sitter universes for the time dimension. My assumption is that for the three spatial dimensions this "stacking" is actually a higher-level sphere - that you have little pointy-edged cubes and tetrahedrons (or higher dimensional equivalents) coming together.  Also, is time the one true-blue Euclidean straight line dimension, no extra degrees there?  Then there are the compactified dimensions - do those have to be closed with < 180 degrees in a circle? (I'm out to sea by now)


 * It seems like you give the N=4 super Yang–Mills theory as an example at least three separate times throughout the text, not going into it all that much each time - my feeling is you need to round up those stray sections and condense in one place.


 * The absolute core of the article, "the idea of AdS/CFT", needs beefing up with more specific examples. I just don't get how the boundary of a cylinder looks like a four-dimensional spacetime!  I don't get what sort of calculation on a single ?something? in the anti-de Sitter space looks like multiple particles in spacetime.  This is the door of our perception - get out the cleanser.

Wnt (talk) 02:09, 8 December 2013 (UTC)


 * Thanks for your comments, Wnt. I'm not going to try to edit the content of the article while it's on the Main Page, but here are some answers to your questions:


 * 1. You basically have the right idea about hyperbolic space. If you look at any triangle in the hyperbolic plane (see the picture), then its angles will sum to less than 180 degrees, and the value this sum depends on the size of the triangle. For very small triangles in the hyperbolic plane, the sum of the angle measures will be very close to 180 degrees. Thus the geometry of anti-de Sitter space is approximated by more familiar Euclidean geometry at very short distances.


 * 2. Just as the boundary of the hyperbolic plane is a circle, the boundary of three-dimensional hyperbolic space will be an ordinary two-dimensional sphere, and the boundary of higher dimensional hyperbolic spaces will be higher dimensional spheres (which, obviously, are not so easy to visualize).


 * 3. The example discussed in the article involves three-dimensional anti-de Sitter space. The boundary of this space is not four-dimensional spacetime, but an imaginary two-dimensional spacetime. If you want to model, say, nuclear physics using the AdS/CFT correspondence, then you have to consider an example of the duality where the boundary is four-dimensional.


 * Polytope24 (talk) 03:13, 8 December 2013 (UTC)


 * 1. So to be clear, the "triangles" and "squares" really do have smaller angles, and at any given point there are only 360 degrees.  But, say, if you shine a light down one of the lines of the triangle it will end up going "straight" to the next vertex?  And you could tile our universe with these "tetrahedrons" and "cubes", three cubes around the vertex of a tetrahedron, three tetrahedrons around the vertex of a cube, for a total of I think three cubes and four tetrahedrons meeting at a point?  Is there a way to calculate how big the side of each polytope is?


 * 2. OK, so the anti-de Sitter space is the physical dimensions of our space (not time) ... plus the compactifed dimensions? And time remains a separate dimension orthogonal to everything else, and not subject to any transformations.


 * 3. The boundary of the two dimensional space is a cylinder (counting the time dimension); in space it is a line that wraps around on itself, and the boundary of the four dimensional space would be a three dimensional space that wraps around on itself? Is the geometry/manifold specified by the theory?  And if an infinite anti-de Sitter space has a boundary of finite size, what determines the size of the boundary?  :I still am confused at what actually "lives" in the anti-de Sitter space.  Given the lack of precision of measurements in our space, what is this apparently "infinite resolution" needed for?  (I'm waaay out to sea by now, distant ship smoke on the horizon...) Wnt (talk) 06:23, 8 December 2013 (UTC)


 * if you shine a light down one of the lines of the triangle it will end up going "straight" to the next vertex?


 * The edges of the triangles in the picture are what mathematicians call geodesics. This means that they are as straight as they can possibly be in the curved space.


 * you could tile our universe with [these shapes]?


 * On large distance scales, the real universe is not curved in the same way as anti-de Sitter space, so you can't have a similar hyperbolic tiling of real physical space.


 * the boundary of the four dimensional space would be a three dimensional space that wraps around on itself?


 * Correct.


 * And if an infinite anti-de Sitter space has a boundary of finite size, what determines the size of the boundary?


 * Technically, what we're calling the "boundary" should really be called a "conformal boundary". This is a mathematical notion that makes it possible to have a boundary that's infinitely far from any point in the interior. Also, the boundary theory appearing in the correspondence is a conformal field theory, which means in particular that it is scale invariant, and so one does not need to talk about the size of the boundary. Polytope24 (talk) 07:11, 8 December 2013 (UTC)


 * Great answers so far! And I shouldn't have confused the tiling of the space and the tiling of our universe.  But...
 * Is it necessary for the AdS/CFT correspondence that our universe actually be a closed universe? Of finite size?  With positive curvature, with divergent lines intersecting?
 * An event in the de Sitter space maps to one or more events in our universe. Every point in our universe, this conformal boundary, is infinitely far from the point in de Sitter space where the event occurs, and vice versa.  So why do the events in our universe occur in one tiny region?
 * Wnt (talk) 17:50, 8 December 2013 (UTC)


 * The AdS/CFT correspondence describes gravity only in a certain approximation, so the large scale structure of our universe (and in particular the question of whether it is closed) is not really relevant.


 * I'm not sure if I understand your second bullet. Let me just say that the AdS/CFT dictionary is highly nontrivial. In AdS/CFT, you have physical objects in one theory mapping to a priori completely different physical objects in the dual theory. It's not as simple as events in one description mapping to events in the other. Polytope24 (talk) 19:30, 8 December 2013 (UTC)

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Ashtekar's comments
Please see article:

https://thewire.in/14279/good-scientists-solve-problems-but-great-scientists-know-whats-worth-solving/

Ashtekar, world renound general relativist, has said

"Again, nobody is taking anything away from the successes that the AdS/CFT duality has had; but there is a big gap between the successes and the rhetoric. The rhetoric is at a much higher level than the successes. So, for example, in this conjecture, first of all the space-time is 10 dimensional. The physical space-time is supposed to be asymptotically anti-de Sitter, which has a negative cosmological constant. But we look around us, and we find a positive cosmological constant. Secondly, the internal dimensions in the conjecture, or this definition, are macroscopic. The Kaluza-Klein idea is that there are higher dimensions but because they are all wrapped up and microscopic, say, at Planck scale, we don’t see them. That’s plausible. But here, in AdS/CFT duality, they need the radius of the internal dimensions to be the same as the cosmological radius. If so, if I try to look up I should see these ten dimensions; I don’t. So, it can’t have much to do with the real world that we actually live in. These are elephants in the room which are not being addressed. "

In particular I'd like to draw attention to "they need the radius of the internal dimensions to be the same as the cosmological radius."!

Ibayn (talk) 03:27, 21 April 2017 (UTC)

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Punctuating anti-de Sitter
My orthographic understanding is that the ndash is used when prefixing an unhyphenated compound, so I suggest rendering this as anti–de Sitter, with an ndash. &mdash; MaxEnt 17:19, 16 December 2018 (UTC)

Perturbation Theory
Since Perturbation Theory was in P. A. M. Dirac's The Principles of Quantum Mechanics, Richard Feynman would have had to have done the work before he was twelve. In fact what Feynman got the Nobel Prize for was developing path integrals and Feynman diagrams. His work greatly simplified calculations in Perturbation Theory, but he wasn't one of the developers. Shmuel (Seymour J.) Metz Username:Chatul (talk) 07:14, 1 May 2020 (UTC)