What use is the AdS/CFT correspondence in a flat universe?

[nomadreid]

TL;DR Summary

In popular accounts, the holographic principle relies on having a boundary, which works fine for black holes, but if we are in a universe without spatial boundary, how does that help?

All the accounts which I have read (and which are accessible to my limited knowledge of General Relativity and its mathematics) on the holographic principle says vaguely that the AdS/CFT correspondence is very enlightening, but with the caveat that, well, we don't happen to live in an AdS space, but rather are apparently slowly approaching a deSitter space, but string theory does wonderful and unexpected things. I do not know whether this means that the techniques of the correspondence then is somehow applied to apply to our space, or perhaps to spacetime with the future being a boundary, or whether this is just optimism that a related topic will bear fruit sometime, or what?

 

[PeterDonis]

Moderator's note: Moved thread to the Beyond the Standard Model forum.

 

[king vitamin]

Keep in mind we didn't even know the sign (or finiteness) of the cosmological constant for the first ~80 years of relativistic cosmology, which is to say that it takes very specific and precise experiments to even distinguish small positive/negative/zero cosmological constants from each other. If we consider some localized hypothetical quantum gravity experiment within some region with linear size $R \ll |\Lambda|^{-1/2}$, it might be reasonable to assume that something we could predict from AdS/CFT with $\Lambda < 0$ would be effectively $\Lambda$ independent in the $\Lambda \rightarrow 0$ limit leading to predictions which do not depend on the sign of $\Lambda$ at all. After all, we do not expect a local experiment to depend so sensitively on the boundary conditions of our whole universe!

But in applications to cosmology (length scales comparable to $|\Lambda|^{-1/2}$), then certainly you can object to how useful AdS/CFT predictions are to our universe.

 

[nomadreid]

Thanks, king vitamin. Interesting considerations.

 

[atyy]

There are attempts to make AdS/CFT relevant to our universe. Here is a recent example.

https://arxiv.org/abs/1907.06667
Cosmology at the end of the world
Stefano Antonini, Brian Swingle
In the last two decades the Anti-de Sitter/Conformal Field Theory correspondence (AdS/CFT) has emerged as focal point of many research interests. In particular, it functions as a stepping stone to a still missing full quantum theory of gravity. In this context, a pivotal question is if and how cosmological physics can be studied using AdS/CFT. Motivated by string theory, braneworld cosmologies propose that our universe is a four-dimensional membrane embedded in a bulk five-dimensional AdS spacetime. We show how such a scenario can be microscopically realized in AdS/CFT using special field theory states dual to an "end-of-the-world brane" moving in a charged black hole spacetime. Observers on the brane experience cosmological physics and approximately four-dimensional gravity, at least locally in spacetime. This result opens a new path towards a description of quantum cosmology and the simulation of cosmology on quantum machines.

 

[Demystifier]

Summary:: In popular accounts, the holographic principle relies on having a boundary, which works fine for black holes, but if we are in a universe without spatial boundary, how does that help?

All the accounts which I have read (and which are accessible to my limited knowledge of General Relativity and its mathematics) on the holographic principle says vaguely that the AdS/CFT correspondence is very enlightening, but with the caveat that, well, we don't happen to live in an AdS space, but rather are apparently slowly approaching a deSitter space, but string theory does wonderful and unexpected things. I do not know whether this means that the techniques of the correspondence then is somehow applied to apply to our space, or perhaps to spacetime with the future being a boundary, or whether this is just optimism that a related topic will bear fruit sometime, or what?

In practical applications, AdS/CFT is not used to study gravity. It is used to study systems without gravity, such as a flat (3+1) dimensional world without a boundary. The idea is that our (3+1)-dimensional world (with gravity neglected) is mathematically related to a fictional (4+1) dimensional world with gravity, such that our flat (3+1) world is a boundary of the fictional (4+1) dimensional world. It then turns out that some strongly interacting systems in the real (3+1) world (e.g. high temperature superconductivity or quark-gluon plasma) can be more easily described by using the fictional (4+1) world. But it should be stressed that those (4+1) descriptions are approximate descriptions, not exact descriptions, of the original (3+1) system in the real world. Nevertheless, in some cases such an approximation turns out to work better than other known approximations.

 

[haushofer]

It produces a lot of citations.

 

[Demystifier]

It produces a lot of citations.

Does it refer to my post? If so, then I fully agree.

 

[haushofer]

Does it refer to my post? If so, then I fully agree.

It was meant as an answer to the question in the opening post :P

 

[nomadreid]

Thanks, Demystifier. That helps.

 

[Demystifier]

Thanks, Demystifier. That helps.

For a readable practical introduction to AdS/CFT I can also recommend http://de.arxiv.org/abs/1409.3575

 

[nomadreid]

Super, Demystifier. I have downloaded it; it looks good. Thanks again.

 

[haushofer]

The string theory book (2nd edition) by Zwiebach also contains a very pedagogical intro to ads/cft.

 

[McFisch]

I'ld say there are several ways in which AdS/CFT could be relevant. The first was mentioned already by @Demystifier : To study the dual field theory. Even if that requires conformal symmtery (which is not present in our (low energy?) theories), one might still consider our standard model as a perurbed conformal field theory.

The usual answer I read in introductions is usually this: As a starting point ("toy model") for later applications. There are already models out there that try to establish holography between a field theory and flat spacetime. Instead of the spatial boundary one conciders the null boundary at lightlike infinity.