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Anonymous at Sat, 22 Jun 2024 19:55:54 UTC No. 16248006
Can someone explain what "anti-de Sitter/conformal field theory correspondence" means
Anonymous at Sat, 22 Jun 2024 19:58:30 UTC No. 16248010
Yes, but not to a "onions jack" poster.
Anonymous at Sat, 22 Jun 2024 20:15:01 UTC No. 16248030
>>16248010
please elaborate
Anonymous at Sun, 23 Jun 2024 02:25:52 UTC No. 16248634
>>16248006
The answer, apparently, is no. No one here can explain AdS/CFT to you.
Anonymous at Sun, 23 Jun 2024 05:19:05 UTC No. 16248788
>>16248006
A schizophrenic quantum gravity proposition that only passed (((peer review))) due to string theorist nepotism that is propagated as the best physical maxim of the past twenty years. Seriously, name one (1) string theory paper that's failed peer review. They're a tight knit community who accept and cite each other as infinitum implying people like maldacena (theorist with no experimentally validated models) have more citations than people like Higgs and more citations than fucking experimental CERN papers (which are notorious for being cited in all experimental and theorist papers related to the topic). If you can't see the issue here then you're helpless.
Tldr it's a literal grift.
Anonymous at Sun, 23 Jun 2024 07:22:24 UTC No. 16248900
(1/4)
lets start with anti desitter spaces.
If you imagine a surface with a grid on it, its natural to imagine all the grid-lines making right angles with eachother at points of intersection. This we'll consider to be a symmetric surface. Its easy to imagine this when the grid is flat, but desitter spaces describe surfaces which have a curvature. Desitter space has a positive curvature, like a ball, so the grid cells will appear bloated when projected onto a flat surface. Anti desitter space has a negative curvature, hyperbolic, with reachable space getting further away from itself as you traverse a distinct path. If on a ball, parallel lines will intersect as they move straight, in anti desitter space they will get further away from eachother as they move straight. Now try to project this onto a flat plane. Where as a globe will have its points away from the center get stretched out and widened (think greenland), anti desitter space will have points away from the center get crunched closer together for the projection to be able to account for the increased amount of space. It functions like a binary tree, duplicating more and more as you move from your starting location, but not exactly because the right angle principle mentioned at the beginning has to be obeyed. So on the edges of a 2d projection of anti desitter space you end up with an infinite number of points along the rim. It is this boundary of infinite points that becomes important for conformal field theory.
Anonymous at Sun, 23 Jun 2024 07:23:43 UTC No. 16248903
>>16248900
Conformal field theories are models for determining the allowable motion a quantum particle can participate in. They effectively challenge you to find a set of consistent behaviors (matrices) so long as they are angle preserving. Angle preservation is important because a quantum state is just a vector specifying how much is being contributed to each particular dimension, so if in the starting state two dimensions had no overlap/influence on eachother then the angle preserving property will make sure they still dont after the motion/transformation occurs. Besides that, feel free to find any transformations which are self consistent and agree with experiment. YangMills theories for example put on some more constraints like ensuring the "area" spanned by the quantum state (its determinant) does not change (shrink/stretch) under the transformations, and that all transformations preserve the Lagrangian. Turns out, with these constraints, the remaining 1x1, 2x2, and 3x3 matrices describing possible motion/transformation correspond to the electromagnetic, weak, and strong forces, respectfully.
Anonymous at Sun, 23 Jun 2024 07:24:53 UTC No. 16248907
>>16248903
(3/4)
So now, on the boundary of this desitter space, with its infinite points, each point actually serves as a map of the path taken from the center of the space to get there. Imagine starting at the center of the binary tree and making a left/right decision as you take an infinite path toward a boundary point. That boundary point therefore is a single label for the path you took, like "LRRLRLLLLRRLR...". On the boundary, only aware of the boundary points themselves, will be a CFT with rules governing the motion between states, but on the inner hyperbolic surface will be gravitational theory dictating which left/right path you have to take. Turns out these two descriptions are equivalent/dual under this visualization. They both describe the same thing. One describes how a quantum particle will have to move under a gravitational influence, while one is just a field theory moving between states.
Anonymous at Sun, 23 Jun 2024 07:26:30 UTC No. 16248909
>>16248907
(4/4)
It may help to know that the motivation for this came from the horizon problem of black holes. Under pure relativistic principles, there should be no significant physical distinction of the horizon; the part where it goes black. As far as space time is concerned, it remains smooth and continuous through that radius. However when it was discovered that the entropy/information contained within a black hole scales with the radius squared (not cubed) this implied that all the information contained within it has to correlate to its surface, and not its bulk. Because black holes have entropy this actually means they have a temperature and indeed radiate. When a quantum fluctuation occurs on the edge of a blackhole's horizon, one part of the particle/antiparticle pair may be sucked into the blackhole while the other is left outside. With these particles being entangled at the source, the point of their appearance on the surface of the blackhole's horizon and the trajectory taken into the singularity by the particle internal to the radius must be correlated. Hopefully the similarity to the ads/cft correspondence is clear enough.
I made all this up btw
Anonymous at Mon, 24 Jun 2024 00:15:12 UTC No. 16250088
>>16248909
youre a great person seriously
Anonymous at Mon, 24 Jun 2024 00:38:41 UTC No. 16250111
>>16248006
https://jsbin.com/locaderuxe/edit?h
Here's a simple easy JS I made (I cheated, AI did) to explain the relations between AdS and CFT