AdS/CFT conjecture is wrong

Depending on how much time I am willing to allow to this subject this might become rather long… It could be of the length of a book if it really wants to cover all the aspects in which string theory is plain wrong but I want to insist also on the way of thinking that brought us into working so long on an idea that is wrong. First, experiments… it is not a direct or trivial problem because models have parameters and various parameters can give different fits and different fits can fit for good or bad with various experimental data… Then, of course it is the corruption at the level of string theory research and the willingness to declare something utterly nonsensical as “well fitting to experiment”… This happens not only in string theory but because string theory is SO wrong it is certainly the place where you see it most. Then, there is the notion of “observability”. Not all objects are in all circumstances observable. You can speak of position for example as an observable and of course you can say a car is 2 meters away from a building. This sentence has some meaning associated to it. It is “well defined” in the context of classical mechanics and classical mathematics. However, the position of a quark in a nucleus is not a well defined statement. The lack of a “precise definition” has various origins. First, due to the generally accepted model of strong interactions a quark is not observable. That doesn’t mean it’s not physical. You can probe it in various ways but a single quark is not defined by itself. This means you hardly can talk about the position of a quark or even less about its speed. Nor can you talk about collective properties of quarks in the same way. For example in order to define viscosity of a quark fluid you may have to define other concepts that have a meaning and are observable. Using some models you can extract some data about whatever you choose to call “viscosity” in your new, extended dictionary. You see, there is a choice and it is not physical. It is a choice of your way of talking. The “way of talking” is essential in almost any formulation of any field of science, from quantum mechanics to general relativity or string theory. You can chose sections of fiber bundles and define adjoint representations etc. but you see, all is dependent on a choice and on a way of speaking. This is why people tend to say fashionable nonsense in scientific journals (targeting a broader audience)… They usually play on the card of having words that sound familiar but are not well defined in the context that is common knowledge… (I said this is going to become hard)… We all know in quantum mechanics are so called “incompatible observables”… what that means essentially is just that they are associated to operators that don’t commute and that means they do not have a common set of eigenvalues (they cannot be diagonalized simultaneously). This is the quantum mechanical way to tell us we must be careful when speaking about two such “observables” at the same time. They are in general non independent in any description. This is another method of tricking the audience. So, we see now that objects that are well defined in some context may have a non-trivial derivation in some other context. Now we can start talking about the first “experiments” trying to give some data that is in accordance to AdS/CFT duality. I spoke quite some time about the “holographic principle” and why “the universe is not a hologram” (not even remotely)… Scaling properties of the holographic principle are in general not obeyed by nothing. Mainly fermions disobey them, reason for which many “corrections” have been introduced… needless to point out how pointless they were… Anyhow, one of the applications of AdS/CFT was to something called the “superfluidity of quark gluon plasma”… In fact this was also an idea of mine, unfortunately never published, when I was in Troy, NY… I just thought loudly about “using AdS/CFT for superfluid layers”… the reaction was : “oh, why didn’t I think at that?” (lol)… never mind, the idea was funny but the results were obviously wrong… You can derive solutions for the strong coupling of a field theory describing quark-gluon plasma using some weakly coupled gravity duals and find out that the viscosity of the system is low… however, the same solutions can be found using other models for the interactions that appear at a “more fundamental” level… so, precisely because the viscosity is not a directly defined quantity you cannot in principle say which formulation is right. Now, however, there is another problem, namely that you can in principle say what is the behavior of some other quantities that are directly measured and AdS/CFT is giving predictions for that. Compared to the experiments these predictions are WRONG! There is absolutely NO WAY TO ARGUE WITH THIS DATA! THEY ARE GODDAMN WRONG! No matter how you change the parameters of the fit you simply don’t get anything like that from AdS/CFT, not even by playing god and giving up the rest of physics just so your model works out! NO! Maybe the best expression for this is given by Feynman : Now, they can be wrong in several ways, one of which is of particular importance for me… and it has to do with something called “large N expansion”… N is the N in SU(N) and it essentially is a trick you use in order to make an expansion in a small parameter on the “other side” of your duality. N=3 is the case for QCD. Now, during my master presentation in paris I remember quite well I discussed about this problem with someone teaching string theory and after 3 hours of lecture which I understood better than he did (apparently) the conclusion was that N=3 is LARGE! Or, at least large enough such that only small corrections could affect the leading term. So, you may apply AdS/CFT in that form whenever 3=infinity… oookkk… no, I mean, as a young wanna be string theorist with lots of arrogance towards the establishment you may swallow that kind of things… the problem is that nature doesn’t and your series becomes at least odd when saying 3=infinity… This however is important in another way too… the large N expansion… I will enter here in some rather technical details… few of you will be able to follow but hey, some may… the N is related to the quark families… In fact if you take an D=4 SU(N) Yang Mills theory with N_{f} quarks and write the renormalization group equation for large N you can redefine the equation using the old yang mills coupling squared and the N above using a single letter and call this new letter your “beta function” … in this way the basic “flow” of your redefined coupling becomes independent of N. So, in large N limit we can use this new “coupling”. Then your fields live in the direct representation and gluons and some ghosts in the adjoint representation. Now, we can go to the so called “t’hooft” diagram. Take a specific scale and then rescale. You will get a factor 1/N for every quark or ghost propagator and a factor of N for every vertex. Every index loop gives a factor of N too… What you may observe is that you get the Euler number : chi=F-E+V factors of N. F= loops, E= edges, V=vortices. How did we end up with this? Well, first of all remember that we speak about gluons and quarks. Quarks live in the direct representation while gluons in the “adjoint” (say dual) representation (obtained by linearizing the action of the group). This means in principle that gluons carry two color indices (being in the dual representation they are obtained as linear combinations). Now, in this representation one splits the diagram such that the color indices associated to the lines are not “lines” but “bands”… and looks at them as if they were simplicial complexes that map a surface with a given topology. In this way we end up with a partition function that is in the form of a series expansion of topological genera. Where are the problems? Everywhere: while mathematically ok-ish one forgets completely what one wants to describe… namely some form of QCD… that’s where we started from. The separation of the dual representation of the algebra over the indices may give you a topological object but that object has no meaning in the sense of QCD… it is NOT ISOMORPHIC. It is at best a dimensional extension over indices of the lines which HAVE NO PHYSICAL MEANING AT ALL! In fact it ruins the original group structure and it gives a sense ONLY when N-> Infinity… Now, after smoking lots of… whatever… you end up believing that N=3 is infinity… case in which the expansion would still be inexact as even in this case there is no isomorphism between the two. Why, I can twist the bands… I can make lots of extra structure after modifying the “dimension” in this way… But that’s me speaking, let’s have the experiments talk… Image The obvious result is that experiment is WAY OFF any AdS/CFT prediction and that’s the way they should be… Now, caveat: here we are dealing with a theory that is QCD in nature… so, the place where all the AdS/CFT duals started … QCD has some features: it is a sort of extension of Yang Mills which is non-abelian, it has quarks and gluons and confinement (if any)… these features make QCD a GOOD candidate for testing AdS/CFT… anyhow, far better than any many electron system around… and it fails Now, let’s go further and see how AdS/CFT duals can help condensed matter theorists (rumors of condensed matter people feeling targeted, crowding at the borders in a desperate escape tentative)… The “help” of AdS/CFT people (although I bet nobody asked for it) is to identify gravity duals to conformal field theory problems in condensed matter… If you understand the words you already see they don’t sound well… dual mapping is coming with a great deal of baggage from the gluon self-energy diagrams… I mean GLUONS! There are no gluons in condensed matter… and why on earth should N-> infinity there? Ok, string theorists will tell you that the “holographic idea” is more than AdS/QCD… it is so fundamental that you couldn’t eat your breakfast without it or at least without a black hole in the dual bulk… fact is, however, that nature proved this as being rubbish… and this is the end…


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