Emergent Space/Time: AdS/CFT and dS/CFT

In summary, these papers seem to suggest that it is possible to analytically continue results in AdS to dS, but that the results have problems.
  • #1
atyy
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https://www.physicsforums.com/showpost.php?p=3263502&postcount=94
mitchell porter said:
At the moment, it only works properly for an emergent AdS space, but if the dS/CFT correspondence can be understood, then this will be true for spaces of positive curvature as well. (In dS/CFT the boundary is purely spacelike and lies in the infinite past and future, rather than being timelike as in AdS/CFT, so it's as if the timelike direction in the Lorentzian gravitational space is emerging from Euclidean field theory on a sphere in the infinite past.)

Actually, thinking even about AdS/CFT which is commonly said to be emergent space, but not emergent time, if the bulk geometry is pseudo-Riemannian, which has multiple timelike directions at each point, shouldn't time emerge too?
 
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  • #2
I think one wants a non-unitary CFT that has a unitary renormalization group flow. Whatever that means.
 
  • #3
What, what, what? :rofl: Can a layman get an explication?
 
  • #4
See http://arxiv.org/abs/hep-th/0106113" [Broken]. "In general the dual CFT may be non-unitary". But we want, or we think we want, the bulk theory to be unitary, and since it is defined by RG flow in the "RG space" of the boundary CFT, PM wants "unitary RG flow" in that space. Ultimately it may not be the right way to put it, but I know what he's saying.
 
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  • #5
mitchell porter said:
See http://arxiv.org/abs/hep-th/0106113" [Broken]. "In general the dual CFT may be non-unitary". But we want, or we think we want, the bulk theory to be unitary, and since it is defined by RG flow in the "RG space" of the boundary CFT, PM wants "unitary RG flow" in that space. Ultimately it may not be the right way to put it, but I know what he's saying.

A CFT sits a a fixed point(its scale invariant) by definition so presumably once one flows from the fixed point the theory is no-longer a CFT but some perturbation of it in a relevant direction??
 
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  • #6
That thought was bothering me even as I wrote. I guess that for both conformal and nonconformal boundary theories, the AdS radial dimension encodes behavior at different scales, but for the conformal case, one shouldn't speak of "flow".
 
  • #7
Of course it is true that a CFT doesn't itself flow, but it does have a spectrum of operators and controls the flow in its vicinity. In any event, my statement was colloquial and meant for pure amusement.

Unitarity in the RG flow is a strange thing. I would expect it to be connected to operators with imaginary dimension [tex] \Delta [/tex], something not unfamiliar from non-unitary CFTs and other exotica. This way when you flow for an "RG time" T you find expressions like [tex] e^{\Delta T} [/tex] which now look more like unitary evolution if [tex] \Delta = i |\Delta |[/tex]. Hence RG time becomes real physical time!

I think this is well known wild speculation, but it is not much more than that right now.
 
  • #8
Thanks guys! Actually, I was thinking of something presumably simpler. Lorentzian spacetimes have "time" or "times" that Riemannian spacetimes don't. In AdS/CFT, what in the boundary theory determines the signature of the bulk geometry?

Papers like http://arxiv.org/abs/0804.3972 and http://arxiv.org/abs/0804.4053 seem to have Galilean boundary theories with Lorentzian bulk, so I presume it isn't the signature of the boundary that determines the bulk signature? (Or is this some weird thing that condensed matter folks do that "real" string theorists wouldn't contemplate?)
 
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  • #10
Just speaking classically, de Sitter space has a spacelike conformal boundary, anti de Sitter has a timelike conformal boundary, and Minkowski space has a lightlike conformal boundary. (When I say the AdS boundary is timelike, I mean it has a timelike direction - it has spacelike directions too.) Also, of course, the bulk theories all have Lorentzian signature, classically.

I read somewhere that results in AdS can sometimes be analytically continued to results in dS by way of working in Euclidean signature in the AdS boundary theory, but the dS "results" had problems as usual - maybe they were purely formal expressions; I forget the details.
 

1. What is Emergent Space/Time?

Emergent Space/Time is a theory in physics that suggests the existence of space and time is not fundamental, but instead arises from the interactions of underlying quantum building blocks. This theory is often used in the context of AdS/CFT and dS/CFT, which are mathematical models that relate gravitational theories in anti-de Sitter (AdS) or de Sitter (dS) space to conformal field theories (CFTs) on the boundary of that space.

2. What is AdS/CFT?

AdS/CFT stands for Anti-de Sitter/Conformal Field Theory and is a theoretical framework that relates a gravitational theory in AdS space to a CFT on the boundary of that space. This theory is based on the holographic principle, which suggests that all the information contained in a volume of space can be encoded on its boundary. AdS/CFT has been used to gain insight into the nature of black holes and the behavior of strongly interacting systems in physics.

3. What is dS/CFT?

dS/CFT stands for de Sitter/Conformal Field Theory and is a theoretical framework similar to AdS/CFT, but instead relates a gravitational theory in de Sitter space to a CFT on its boundary. This theory has been used to study the behavior of the universe at large scales, such as the accelerated expansion of the universe.

4. What is the relationship between AdS/CFT and dS/CFT?

The relationship between AdS/CFT and dS/CFT is still an area of active research, but both theories are based on the holographic principle and suggest that a gravitational theory in a particular space can be described by a CFT on its boundary. Some scientists believe that there may be a duality between the two theories, meaning that they are two different descriptions of the same underlying physical system.

5. How does Emergent Space/Time relate to our understanding of the universe?

Emergent Space/Time, along with AdS/CFT and dS/CFT, provides a different perspective on the nature of space and time than the traditional theories of general relativity and quantum mechanics. It suggests that these concepts may not be fundamental, but instead arise from the interactions of more fundamental building blocks. This theory has the potential to help us better understand the behavior of the universe at both small and large scales, as well as potentially reconcile the seemingly incompatible theories of general relativity and quantum mechanics.

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