UV-IR Corresp: AdS-CFT & Non-AdS Differences

[lwjjack]

Hi everyone
Days ago I posted a thread here about UV-IR relationship and so far got no reply,so instead I would like to gather some information on what role UV-IR correspondence should play in AdS-CFT and the difference between non-AdS and AdS correspondence.

 

[mitchell porter]

I have no time to reply to this in any coherent way. But

https://arxiv.org/abs/hep-th/9805114 by Susskind and Witten

is the original paper on the UV-IR correspondence.

Essentially, to describe bulk physics in a small patch of AdS space, only requires infrared information about the boundary theory, i.e. long wavelength behavior. But the larger the AdS patch that you want to describe, the further you must go into the ultraviolet of the boundary theory. When you have no UV cutoff at all, at that point you're describing AdS all the way out to the boundary.

The logic of this may be glimpsed, by thinking about how Plato's cave is used as an analogy for AdS/CFT. A point in AdS space "casts a shadow" on the boundary, in the form of a wedge made of all the spacelike paths from the point to the boundary. The closer to the boundary, the smaller the wedge is. The physics at the point in the AdS bulk, can be expressed as an integral over the physics at all the boundary points in its "shadow".

Maldacena wrote an article for Scientific American about holographic duality, this would be described informally, somewhere in that article.

OK. So we have that the UV of the boundary theory is needed, in order to describe large patches of AdS space. But you also need large patches of AdS space to describe long-wavelength phenomena in AdS; i.e., phenomena from the IR of the bulk theory. So, in this sense the UV of the boundary theory corresponds to the IR of the bulk theory.

What would be the reverse of this? It would be an "IR-IR correspondence", in which the IR of the bulk theory corresponds to the IR of the boundary theory in some sense. The paper from your other thread https://arxiv.org/abs/1801.02589 argues that this is what happens once you are dealing with AdS patches smaller than the radius of the compact dimensions. At that point things get more complicated than just, layers of AdS space being built up by shorter and shorter wavelengths in the boundary theory.

The holographic dual of very long boundary wavelengths is a fully 10- or 11-dimensional patch - we're no longer dealing with a full geometry like AdS_5 x S^5, but something more like a 10-dimensional ball (ball in the sense of topology, a finite patch of R^10) within this space. It's a different regime of the duality, which they seem to explain in terms of numerous short strings condensing into long strings and thereby losing degrees of freedom.