As the saying goes, a picture speaks a thousand words, but since links and image sources have a tendency to deteriorate over time, let me spell it out for you: The AdS/CFT scaling does not agree with the data at all.
The basic message is that AdS/CFT fails to explain the heavy ion collision data about jets at LHC. The model should be able to predict how partons lose their momentum in quark gluon plasma assumed to be formed by the colliding heavy nuclei. The situation is of course not simple. Plasma corresponds to low energy QCD and strong coupling and is characterized by temperature. Therefore it could allow description in terms of AdS/CFT duality allowing to treat strong coupling phase. Quarks themselves have a high transversal momentum and perturbative QCD applies to them. One has to understand how plasma affects the behavior of partons. This boils to simple question: What is the energy loss of the jet in plasma before it hadronizes.
The prediction of AdS/CFT approach is a scaling law for the energy loss E ∝ L3T, where L is the length that parton travels through the plasma and the temperature T is about 500 MeV is the temperatures of the plasma (at RHIC it was about 350 MeV). The figure in the posting of Sabine Hossenfelder compares the prediction for the ratio RAA of predicted nuclear cross section for jets in lead-lead collisions to those in proton-proton collisions to experimental data normalized in such a manner that if the nucleus behaved like a collection of independent nucleons the ratio would be equal to one.
That the prediction for RAA is too small is not so bad a problem: the real problem is that the curve has quite different shape than the curve representing the experimental data. In the real situation RAA as a function of the average transversal momentum pT of the jets approaches faster to the "nucleus as a collection of independent nucleons" situation than predicted by AdS/CFT approach. Both perturbative QCD and AdS/CFT based model fail badly: their predictions do not actually differ much.
An imaginative theoretician can of course invent a lot of excuses. It might be that the number Nc=3 of quark colors is not large enough so that strong coupling expansion and AdS/CFT fails. Supersymmetry and conformla invariance actually fail. Maybe the plasma temperature is too high (higher that at RHIC where the observed low viscocity of gluon plasma motivated AdS/CFT approach). The presence of both weak coupling regime (high energy partons) and strong coupling regime (the plasma) might have not been treated correctly. One could also defend AdS/CFT by saying that maybe one should take into account higher stringy corrections for strings moving in 10 dimensional AdS5× S5. Why not branes? Why not black holes? And so on....
Could the space-time be 4-dimensional after all?
What is remarkable that a model called "Yet another Jet Energy-loss Model" (YaJEM) based on the simple old Lund model treating gluons as strings in 4-D space-time works best! Also the parameters derived for RHIC do not need large re-adjustment at LHC.
4-D space-time has been out of fashion for decades and now every-one well-informed theoretician talks about emerget space-time. Don't ask what this means. Despite my attempts to understand I (and very probably any-one) do not have a slighest idea. What I know is that string world sheets are 2-dimensional and the only hope to get 4-D space-time is by this magic phenomenon of emergence. In other worlds, 3-brane is what is wanted and it should emerge "non-perturbatively" (do not ask what this means!).
Since there are no stringy authorities nearby, I however dare to raise a heretic question. Could it be that string like objects in 4-D space-time are indeed the natural description? Could strings, branes, blackholes, etc. in 10-D space-time be completely un-necessary stuff needed to keep several generations of misled theoreticians busy? Why not to to start by trying to build abstraction from something which works? Why not start from Lund model or hadronic string model and generalize it?
This is what TGD indeed was when it emerged some day in Octorber year 1977: a generalization of the hadronic string model by replacing string world sheets with space-time sheets. Another motivation for TGD was as a solution to the energy problem of GRT. In this framework the notion of (color) magnetic flux tubes emerges naturally and magnetic flux tubes are one of the basic structures of the theory now applied in all length scales. The improved mathematical understanding of the theory has led to notions like effective 2-dimensionality and stringy worlds sheets and partonic 2-surfaces at 4-D space-time surface of M4×: CP2 as basic structures of the theory. About this I have told in quite recent posting.
What TGD can say about the situation?
In TGD framework a naive interpretation for LHC results would be that the colliding nuclei do not form a complete plasma and this non-ideality becomes stronger as pT increases. As if for higher pT the parton would traverse several blobs rather than only single big one and situation would be between an ideal plasma and to that in which nucleuo form collections of independent nucleons. Could quantum superposition of states with each of them representing a collection of some number of plasma blobs consisting of several nucleons be in question. Single plasma blob would correspond to the ideal situation.
In TGD framework where hadrons themselves correspond to space-time sheets, this interpretation is suggestive. The increase of the temperature of the plasma corresponds to the reduction of αs suggesting that with at T=500 GeV at LHC the plasma is more "blobby" than at T=350 GeV at RHIC. This would conform with the fact that at lower temperature at RHIC the AdS/CFT model works better. Note however that at RHIC the model parameters for AdS/CFT are very different from those at LHC: not a good sign at all.
I have discussed the TGD based explanation of RHIC results for heavy ion collisions and the unexpected behavior of quark-gluon plasma in proton-proton (rather than heavy ion) collisions at LHC here. See also the blog posting about LHC results.
The application of AdS/CFT duality to condensed matter is the most recent fashion. Good luck! This is certainly needed. And a lot of funding too! It is quite a challenge to describe the complexities of condensed matter physics in terms of strings, branes, and black holes in 10 dimensions! But certainly one could invent less clever ways to spend one's time.