AdS/CFT: any significant quantitative success?

[petergreat]

I've heard a lot about AdS/CFT lately as an approach to solve strongly coupled field theories such as QCD and condensed matter systems. However I am left wondering whether AdS/CFT has produced any quantitative result that is either i) not obtainable from previous methods, or ii) significantly less demanding in computing power than, say, lattice QCD?

 

[marcus]

I've heard a lot about AdS/CFT lately as an approach to solve strongly coupled field theories such as QCD and condensed matter systems. However I am left wondering whether AdS/CFT has produced any quantitative result that is either i) not obtainable from previous methods, or ii) significantly less demanding in computing power than, say, lattice QCD?

Hermann Nicolai has an article about this. He is a prominent European string theorist.
My impression was that string math has NOT produced anything on QCD that was not already obtainable (as you said) but that it's nevertheless useful. It opens up alternative methods of computing that may be superior in some cases. I'll try to find links to Nicolai's writings about this.

Here is one piece he had in Nature, October 2007
http://www.nature.com/nature/journal/v449/n7164/full/449797a.html
A PF member kindly posted a few selected excerpts so you can see the main thing the article says:
https://www.physicsforums.com/showpost.php?p=1473963&postcount=11

 

[ap_nhp]

It has one success can be observable is the result of Prof Dam Thanh Son in physical review letter 2005 about viscosity/entropy ratio in strongly interacting system.

 

[humanino]

My impression was that string math has NOT produced anything om QCD that was not already obtainable (as you said) but that it's nevertheless useful.

From gauge-string duality to strong interactions: a Pedestrian's Guide
Ann.Rev.Nucl.Part.Sci.59:145-168,2009

The role of the gauge-string duality in our understanding of the strong interaction is still evolving. The duality has made an indelible mark on our understanding of QCD, and it offers uniquely geometrical perspectives on confinement and the quark-gluon plasma. However, it has not solved QCD.

So, there is on one side people trying to solve QCD who have not (yet ?) succeeded, and there are on all other sides people trying to model QCD for whom the geometric perspective offered by Maldacena is most inspiring. I'll quote a little more from the conclusion of the above review.

The gauge-string duality [...] falls short [of describing strong interactions]. [...] Yet, constructions that use classical gravity and probe branes provide an excellent venue for calculations ranging from meson spectra to transport coefficients. Finite temperature is elegantly included in these calculations in terms of a black hole horizon in the fifth dimension.

Making the comparisons between such calculations and QCD systematic is a persistent difficulty. Despite this difficulty, gauge-string treatments of confinement and of finite-temperature nonabelian plasmas are valuable because they complement insights from more standard quantum field theoretic treatments. For example, the descriptions of confinement are elegant and geometrical, the connection to hydrodynamics is relatively simple, and the interplay between hard probes and a thermal medium is rich and explicit.

 

[Physics Monkey]

Hi petergreat,

Using AdS/CFT to study strongly interacting systems is still in its infancy, but let me give you some of the highlights so far in my opinion. AdS/CFT has provided quite a few qualitative insights. Here are a few examples:

1. The idea that viscosity and entropy density should be strongly related is a product of AdS/CFT. In particular, there is a conjectured bound on the ratio $$\eta / s$$ ($$\eta$$ is the viscosity) which is supposed to be bigger than $$1/(4\pi)$$. We now know this bound is not true, but it did inspire people to look at this quantity which is very natural from the gravity point of view. The quark gluon plasma at RHIC and cold fermions at unitarity come close to this "bound".

2. AdS/CFT provides a new geometrical picture of confinement. In fact, I've heard many people say that if we hadn't already discovered confinement, we would have learned about it from AdS/CFT. This illustrates one of the key hopes of the AdS/CFT community, namely, that we might learn about qualitatively new dynamical phenomena at strong coupling.

3. AdS/CFT gives a beautiful geometrical picture of entanglement entropy in the field theory. The gravity calculation is incredibly easy compared to the field theory calculation, but I think it hasn't yet led to really interesting progress on the field theory side. However, the interplay of quantum information theory and gravity is just beginning to be understood in the context of AdS/CFT.

4. AdS/CFT really shines in real time transport at finite temperature. These calculations are extremely difficult in the field theory because of subtleties in analytic continuation, etc that arise. I personally think one of the major contributions of AdS/CFT will be to the study of real time response and non-equilibrium phenomena at finite temperature in field theory. But this area is still very young.

I focused on the positive, but AdS/CFT is still a long way from making contact with really real systems. The closest so far may be the quark gluon plasma where some quantitative predictions of the theory may be more or less borne out. Other condensed matter systems still seem quite out of reach, despite the motivations of many people in the field. We best understand translation invariant highly supersymmetric situations at large N, strong coupling, etc, which are relatively far from systems like cuprate superconductors or heavy fermi liquids.

Of course, we are learning a great deal about quantum gravity as well!

Hope this helps.

 

[tom.stoer]

The key question is whether AdS/CFT is 1) a new computational toolbox for no-perturbative (S)QCD, or whether it is 2) a model for quantizing gravity and harmonizing it with other interactions.
For 1) the current status of AdS/CFT is fine, but for 2) rigorous proofs are missing.

For me it is still unclear what the implications of the famous dualities really are: is the standard model with QCD a low-energy effective QFT derived from some string theory model (lie AdS/CFT)? Or is string theory a large-N approximation of QCD?