Bert Schroer has a new version of his paper that was discussed here earlier this year, now with the amended title String theory and the crisis in particle physics (a Samizdat on particle physics). He claims that the version reflects a change in viewpoint due to his participation in this and other weblogs, and I believe he would like the opportunity to discuss this further here. There’s also a posting about this at the weblog of Risto Raitio.
Update: Schroer, agreeing with his critics that his paper had too many typos, has sent me a corrected version, which is available here, for use until the arXiv version gets updated. He also agrees that an “s” should be a “z” in Samizdat…
Update: Schroer has a new paper out, which contains a review of AQFT and a discussion of light-front holography, with further comments on the relation to the Maldacena conjecture.
I don’t believe that an enemy of my enemy is necessarily my friend. Not even if his essay is free of typos. Bert Schroer is notorious for bizarre behavior at research seminars, conferences and other public occasions, not unlike this forum’s favorite Harvard faculty member. His science (algebraic field theory) suffers from the same ailments as string theory and, in addition, nobody cares about it. His fascination with Pascual Jordan, a discredited Nazi physicist, who (after his “rehabilitation”) pushed for remilitarization of Germany and questioned postwar borders in Europe is truly puzzling: it is like emphasizing that Hitler was really a decent painter…
Yes, I find it fascinating that the protagonist of QFT (the unsung hero of QFT according to Schweber’s historical book on QED) who was point-right on quantum physics could be so dead-wrong in his political ideology (by the way, differnt from Heisenberg who was the leader of the uranium club, Jordan was an absolutely useless figure for the Nazis, that is why they banned him to Rostock).
Sorry for keeping a distance to the “good guys (we) against the bad guys (them) or “who is not with us is against us” . I think that human nature is more complex than that.
I have not attended any conferences for ages and I am not responsible if I appear in the blogges fantasies.
Bert,
Can I ask you whether AdS/CFT is a conjecture or a theorem?
The AdS-CFT is a rigorously established structural theorem of QFT.
The Maldecena idea that particular (beta=0 and hopefully conformally invariant) SUYM models link up with certain strings in 5 AdS dimensions in a certain limit N –> infinity is a conjecture which is in apparent conflict with what the structural theorem says.
What renders the situation difficult is that even if there is a conformal invariant SUYM CFT, the N—> infinity is an object which does not enjoy the status of a QFT. The big question is whether people who do some approximate calculations have the correct interpretation as the AdS correspondent of their (alleged) conformal QFT.
Dear Bert,
If the N -> infinity limit produces something that is not a QFT than how is the rigorous methods of AQFT are in any position to judge the Maldacena conjecture? Why don’t honest AQFT people say that “Okay, this Maldacena guy is talking about something which is not a QFT, so we can’t say anything about it, since we are only able to make statements about QFTs and similarly our rigorous structural theorems don’t apply in this case, since our structural theorems only apply to QFTs. Hence we are not in a position to judge the Maldacena conjecture because our tools are not appropriate to this kind of problem.” ?
Dear Graduate:
The AdS/CFT is a conjecture with a lot of supporting evidence going for it. Wether you cal lthe evidence overwhelming or not depends on personal opinions. So far no one has found a “contradiction”, and the number of tests that have beeen performed is huge.
The “structural theorem” that Bert refers to makes no mention of quantum gravity, so it explains nothing in the AdS/CFT.
The structural theorem, as far as I understand it says: the conformal group is SO(d,2). Therefore
the physical spectrum of the CFT is classified by unitary irreducible representations of SO(d,2). A field theory in AdS willl have the same symmetry group, therefore the two are equivalent. It also gives no information of the dictionary between both sides.
I’m sure Bert can give you a more technical essay on what the theorem means and he will very likely disagree with my assesment of those results.
If the correspondence were just that, it woud have been discovered very quickly and people wouldn’t be working hard trying to understand it.
I think regarding the AdS/CFT, Bert is just wrong.
Sorry to spoil the anti-sting party.
Best,
David B.
No, the theorem is not just a relation of spacetime symmetry groups (this and the ensuing equality of the spectrum was already known way back by Fronsdal) but it is a correspondence between the full QFTs in all their details. It is a bit difficult to express this in terms of standard Lagrangian QFT setting because one of the two sides is non-Lagrangian if the other is. But there is a more general concept of QFT (which is already in constructive use because most of the 2-dim. factorizing models are non-Lagrangian http://br.arxiv.org/abs/math-ph/0601022, http://br.arxiv.org/abs/hep-th/0609130)
Although one side is non-Lagrangian it is still a QFT and not a ST.
So the only saving grace is that the incremental evidence for Maldacena is not given the correct interpretation; perhaps another case demonstrating the conceptual confusion which originates from premature terminology.
Lolka o.k., but isn’t the Maldacena conjecture one which is claimed to involve CFT on one side?
I don’t have the time or inclination to get into a long discussion. However, I did find that wrong statements on the internet have a tendency to percolate to unexpected places, most importantly to the minds of young students. Let me then refer anybody that is interested in true statements about ads/cft (as opposed to various polemics) to the classic review hep-th/9905111, that is a good starting point.
Actually to disconnect this discussion from any attributions of values, if you say that the incremental evidence indicates something deep and contains an important messages, I have no counterargument. Whatever it is, it is defintely not an illustration for a AdS-CFT correspondence about which there exists a rigorous proof (a structural theorem on par with TCP, Spin&Statistics…). If you distingush a conjecture called the Maldacena conjecture (even if I do not understand its true meaning in terms of QFT concepts) from a structurally established AdS–CFT correspondence then all my problems (and may be even yours) are solved as far as the discussion on this weblog goes.
Thomas Larsson Says:
Especially since both sides in the duality seem unphysical. AdS/CFT relates a string theory in AdS space, with negative cc, to an N=4 supersymmetric gauge theory. Last time I checked, neither a negative cc nor N=4 susy were particularly good descriptions of reality.
======================================
Physical reality of both sides is not the point. If at least one side is realistic then it is OK because it can be just a tool. Now you complain that for AdS/CFT neither side is realistic. String theorists and nuclear theorists know it and try to make “some gravity/QCD” version. I think these approaches have given qualitatively satisfactory results so far. It’s not exaggeration at all.
I repeat, there is the maldacena conjecture about a relation between a duality relation between a N–> infinity gauge theory and some form of 5-dim. gravity and there is a mathematical theorem about a AdS–CFT holography (or better correspondenc) and both have, according to our best knowledge nothing to do with each other. From a conceptual point of view the correspondence is rather trivial because the same substrate of matter is only changing its spacetime encoding (for more details see may essay) and olthough the physical interpretation changes it does not change miraculously (e.g. a spin 2 particle must have been there already on the CFT side). If the more than 400 people who worked on this problem would in addition to their computations have leaned back a while and looked at the published theorem may be we would have known by now what the Maldacena conjecture really mean conceptually. But I would predict that nobody at this late time will do this, the right time has passed. Certainly I would not loose time on such a physically fruitless project, but on the other hand as mathematical physicist I find this change of spacetime encoding in holographic projections very interesting; most interesting if the smaller spacetime is not a brane but rather a null-surface (see my last section and the cited literature).
I don’t understand much of your learned discussion but I liked the reference to Leibniz. And please — no smearing by convoluted association. Why should the fact that Pascual Jordan was card-carrying NS party member be at all relevant (except if he threw out important research avenues because they looked ‘jewish’ or something)?
An old Usenet rule went that the first mention of H*tler or He*nlein would immediately end the discussion thread. Beware!
He did not. In fact the reason why despite all his ouvertures he remained a suspicious character to the Nazis was precisely because his publications up to 1934 were overwhelmingly with jewish collaborators. But he was a Nazi and a militarist.
Vafa and collaborators considered Maldacena-type dualities between simpler gauge theories and string theories.
This led to Chern-Simons/topological string dualities, which can be tested in great detail. It all works just fine. The results are so far purely mathematical, but the inner consistency of the underlying ideas is undeniable.
Some comments to Bert Schroer about quantum holography, Chern-Simons action, and null surfaces, or lightlike surfaces, as I have used to call them.
3-D lightlike surfaces in 4-D space-time, which itself is a surface in 8-D space-time H=M^4xCP_2, can be seen as fundamental quantum dynamical objects in Topological Geometrdynamics. They are identified as parton orbits. The effective metric 2-dimensionality with ensuing super-conformal symmetries makes D=4 as a space-time dimension unique.
The infinitesimal transformations respecting null surface property form a Kac-Moody type algebra of conformal transformations of H localized with respect to X^3 decomposing to representations of 1-D Kac Moody algebra.
The cones H_+/-= delta M^4_+/-xCP_2 are also crucial for the formulation of theory and the 3-D lightlikeness of delta M^4_+/- makes possible super-conformal symmetries of new kind based on canonical algebra of H_+/- and its super-counterpart. General Coordinate Invariance predicts quantum holography at level of H_+/-apart from effects implied by the failure of the complete classical determinism of the classical theory.
The resulting theory at fundamental parton is *almost* (absolutely important physically!) topological CFT defined by Chern-Simons action for Kaehler gauge potential of CP_2 projected to X^3. The second quantized fermionic counterpart of C-S action is fixed by the requirement of super-conformal symmetry. The theory allows N=4 super-conformal symmetries of various kinds broken for lightlike 3-surfaces which are not extremals of C-S action (have CP_2 projection with dimension D>3). No space-time (Poincare) super-symmetries and thus no sparticles are predicted.
Super-symmetrization of super-canonical algebra is possible for a sub-algebra of superconformal symmetries for which Noether charges defined as 2-D integrals over partonic 2-surface reduces to 1-D integrals as duals of closed 2-forms. The elements of this algebra has vanishing spin and color quantum numbers and thus leaves invariant the choice of various quantization axis. The vertices of the theory are described by almost topological having stringy character.
Correlations between partons (propagators) involve interior dynamics determined by a vacuum functional defined as a determinant of the Dirac operator and assumed to reduce to an exponent of Kaehler action for absolute extrema playing the role of Bohr orbits for particles identified as 3-surfaces: this is quantum holography at the level of space-time surface. Interior dynamics of space-time surface codes for non-quantum fluctuating classical observables allowing to realize quantum measurement theory at fundamental level.
The mathematical methods of string theory can be applied to TGD and one can see the target space of string theories as a fictive concept associated with the vertex operator construction assigning to the Cartan algebra of Kac-Moody algebra a target space. In TGD framework spontaneous compactification can be seen only as an ad hoc attempt to give physical content to the theory.
For more details see my blog and homepage, in particular What’s New sections to get view about the recent rapidly evolving situation in TGD.
With Best Regards,
Matti Pitkanen
MathPhys
the theorem about the AdS–CFT correspondence does not apply to topological field theories because they lack the notion of localization which is the Faraday-Maxwell origin of the meaning of “field”. Top. field theories strictly speaking are not field theories, they are only called this way because Witten and other people (who view QFT through the functional integral glasses) started to use this metaphoric name. Intrinsically they are combinatorial theories based on tracial algebras and this is also the name mathematicians as Vaughn Jones, Anthony Wassermann,… as well as people in local quantum physics call them. They are so to say the bones of a QFT after you remove the localization flesh to use a metaphoric language. The process how this works is very rigorous but not suited for a weblog.
David B.
I have given more details in may essay and there are 3 important references (not to my own papers). Believe me I would not say something like this and wreck my reputation in public if I would not be completely sure. The theorem has been carefully checked by experts and it has (as I mentioned) the firm status of TCP or Spin&Statistics. I am not disputing that there has been perturbative evidence for something called the Maldacena conjecture, but the interpretation of these calculations in terms of a model illustrating the AdS–CFT theorem (which is a structural theorem valid for all CQT) is metaphoric, it is something else which only a more series conceptual investigation can tell. But this is the problem of the people who do such computation, certainly I will not loose any time on computational details one something which I consider as unphysical as supersymmetry (a social construct in the words of Burt Richter and I agree with him).
Optimist, I did not object AdS/CFT per se, only that people who promote it neglect to mention that in the well-established case, both sides are unphysical. The attitude seems to be that non-stringers should be kept blissfully ignorant about such petty details.
Bert,
Your entire career and that of your best friends, such Swieca, was devoted to the study of simple 2-dimensional models.
These models are at least as far removed from ‘real’ 4-dimesional quantum field theories, as topological field theories are removed from the usual ones.
However, no one stopped you. You did what you could do, and what you wanted to do, and you learnt something from that.
Your critique of Vafa et al is not only irrelevant, but also unfair.
elan
Thinking about when I ever have gotten into an public argument with somebody at a conference, I could only recall one incident at a conference at Lake Tahoe at the begiining of the 90s when there was some brawl with Peter Goddard, the present director of the Princeton IAS. Although he may still hate me for that, I cannot image that he would compare mediocre paintings with Jordan’s creation of QFT and hide behind a pseudonym which is reserved for graduate students and non-tenured colleagues who may fear retaliation as a result of speaking their mind. This would be so absurdly off the standard set by the great Robert Oppenheimer (with whom I had the priviledge of personal contacts during my one year visit of the IAI at the beginning of the 70s) that I have dismissed this idea. And by the way my interest is not fixed on Jordan, I am interested in general in the complexity of humans which show up if a genius scientist outside his area of competence is dead wrong e.g. by supporting the Iraq war (which destroyed an entire country and destabilized the whole world order) http://xxx.lanl.gov/abs/physics/0603095
It is fascinating because it tells us something about the complexity of our own nature (not “them”).
MathPhys and David B.
Your attitude with respect to the Maldacena conjecture and its controversial relation to the AdS—CFT correspondence theorem confirms the main thesis in my essay: when big caravan’s of hundreds of people writing thousands of papers have manufactured a fact then its all over. Nobody will return to a deep problem where he runs the risk of not enjoying the impact increasing community support. An individual researcher in the old-fashioned sense would never ignore such a theorem because it would show his lack of professionality (maybe even lack of intellectual honesty). The problem is not ST in itself as Peter and Lee often state it but rather the stringy metaphoric way of doing particle physics. As anti-Semitism can exist even without Jews, this new accepted metaphoric way of a scientific discourse (and probably will) will be self-feeding without ST. I ask you honestly, would you besides a weblog contribution really sacrifice time and make an effort to study the theorem, its proof and its physical implications? of course not. Why should you, after thousands of publication it has converted into a fact. This is only one illustration of the many conceptual craters which have been left in the landscape of particle physics. As long as things were progressing smoothly, there was no reason to worry about this and now it is not only difficult to cover them in order to be on less swampy conceptual ground, but the present system of scientific production does not support such an activity. Attempts to point out some of the holes are considered to be not sexy (on the scale that ST is).
MathPhys
Sorry, the papers with Swieca (and in part with Voelkel) do not contain minimal models (this was done 10 years later by BPZ) but they do contain the decomposition theory into conformal blocks (called nonlocal components of the local field) in n-dimensions with particular emphasis on the chiral decomposition in two dimensions. This came out from the resolution of a rather deep paradox, the causality paradox of (global) CFT (discussed in previous work) The only model known at that time was the massless exponential Bose field and everything was checked in that example. If you call that unphysical that is your privilege. Whereas ignorance can be combatted, There is simply no remedy against (probably wanton) misrepresentation.
But where did I ever criticize Vafa? I said (in connection with L.B.s death threat against the owner of this weblog) that the ST people should keep their house in order, is this what you mean? It seems that they meanwhile tried, because the real foul ranting has not appeared for some time. Lets see whether they had a sustainable success.
Fortunately physics is one of the most democratic human endeavours.
MatPhys, I have wield no power, I am a retired but still curious physicist, so why do you need the protection of a pseudonym? Be a man and have your outing!
Dear Bert:
I have no qualms about the results you were quoting. It’s just not a proof of the AdS/CFT correspondence.
You want to call it algebraic holgraphy, that ‘s fine by me to.
I meant you were wrong with regards of a proof of the AdS/CFT being available. It’s not. A proof has to contain gravity, or show that it is impossible to do that. Neither of the papers that you quoted explains this to any level.
It is clear that you misunderstood my post and now you are attacking my professionalism and trying to put me down with a rethorical statement. I will not have that, nor will I respond in kind.
It is exactly this attitude in weblogs that makes it very hard to have a real discussion. I might not be the most articulate person, and sometimes what I write can be misinterpreted. That is a risk l take when I post in this kind of forum.
The reason I posted in the first place is to make it clear that the AdS/CFT has not been proved yet, and that you were wrong saying that it has been proved. That is a misleading statement. Something elese was proved. I did not say you were being dishonest, nor lacking in professionalism.
Even professionals can be wrong, and that happens quite often in my experience.
David Berenstein.
Hey David, hope you and yours are doing well, looking forward to seeing you soon. Just a word about your comment- as I indicated above and previously, it is important to correct wrong statements since they spread. I am glad you did that for that “proof of ads/cft”. On the other hand, it is probably not necessary to get into extended discussions with people not really interested in exchange of ideas. Hopefully sometime soon there will be more forums adequate for precisely such exchange, hope to chat with you there.
Dear David, you seem to think that “algebraic” distinguishes it from “field theoretic” but here you are (probably in a large company) misunderstanding what this framework stands for. It has been known that pointlike fields are just algebraic coordinatizations, so it is not a change of content of QFT but just a conceptually very powerful way of avoiding to make a commitment to any particular (composite) field (see Weinberg who way back also became aware of this problem). In your work you have accepted this important step to “intrinsicness” in differential geometry, but you obviously have no familiarity with a more autonomous formulation of QFT which is nothing else but doing the analogous step in QFT. This is not surprising since the new setting (without changing a jota in the physical interpretation of QFT) has taken 2-3 generations to come into the present shape and if one is involved in serious computational work on incremental perfection of the Maldacena conjecture (please no cynism) one does not have the time to immerse oneself into subtle conceptual matters, so this is not an accusation! If you try to find the AdS correspondent of the free massless Bose field (to which the theorem of course also applies) you will understand exactly why one does it that way. I think in the other paper and the lecture Rehren is more reader-friendly and indicates how this can be translated into the setting you are more familiar with. And let me encourage you (since you have strong computational power) to find out what the Maldacena conjecture (as a computational support for a relation of a new object to a particular object called the N–>infinity limit of a CFT, not itself a CFT) could conceptually mean; it is definitly not an illustration of a AdS—CFT correspondence of QFTs (not even in the widest sense of the use of “QFT”)!
And by the way I do not mind if you are a little rough with me (I like young enthusiastic scientists) as long as you do not behave as L.M.
Dear Bert:
I will read those papers carefully.
Regarding notation: I was calling it algebraic holography to distinguish it from gravitational holography. I was not trying to make anything else implied. I was trying to separate the objects of the discussion to avoid confusions.
Now I’ll be signing off this discussion thread.
Best,
David B.
Bert,
The reason I use a pseudonym has nothing at all to do with this discussion which will not get anywhere. Signing off too.
I wish you all the best.
David B., hope to hear of your conclusions whenever you have the time.
David, I understand, this time I misred you. Let me point out that the null-surface holography is much much more interesting than that on (possibly infinitely distant) branes. This type of holography is explained in my CQG article
http://br.arxiv.org/abs/hep-th/0507038
I also reworked the second part which I will send as an replacement probably during this week. This is the case of double cone holography which is closer to the problem of black hole entropy (with some remarks about black hole entropy which could interest you). If you want I can send a copy to your private address, only the reference list has still to be ordered (hope to find time soon). You probably realized that I am a little bit of a loner in the sense that that I do not represent a community and only occasionally collaborate with people who have a similar conceptual-mathematical background. My critical attitude towards string theory is less its content and more the metaphorical way of thinking which it (and other allegedly fundamental proposals) supports. In my essay the fact that it did not lead to predictions is hardly mentioned.
I now understand that you had t’Hoofts vision of holography in the context of gravity in mind; but my use of the word applies to bulk matter in Minkowski spacetime hologaphically projected onto its causal horizon. I think it is not so difficult to understand why this cannot be done in any Lagrangian setting (quantities as entropy have nothing to do with a particular “field-coordinatization). The most important result is that you get a notion of entropy (“localization entropy”) which is consistent with the new quantum local covariance principle (related to background independence) which the string theoretic calculation (and also Weinberg’s vacuum polarization estimates of the cosmological constant) is not.
Pingback: Gravity
In 2002, the two big problems were
http://www.esi-topics.com/brane/interviews/MichaelDuff.html
“What is the theory? How do we make realistic predictions?”
I am somewhat surprised that there was no comment on my emphasis on new contributions (not my own!) in papers which throw considerable doubts on the standard (ST and LQG) mantra that gravity is irreconcilable with QT. In view of
http://br.arxiv.org/abs/gr-qc/0603079
and the development over the last 5 years quoted therein, discussions like that between Sean and Lee look obsolete (and appear a confirmation of my suspicion in may essay that communities are a hindrance to progress).
The main point here is that ,although the emphasis on background independence is very important (the original sin of ST), its implementation through diffeomorphism-invariant states (as in LQG) is misleading. Rather the local covariance principle (diffeomorphism-independence) reflects itself in an algebraic property which (since states are dual to algebras) in terms of states is the invariance of a whole folium of states, but not that of its individual members (these things are explained in previous contributions of the authors). It is precisely the operator Einstein-Hilbert equation which brings about the background independence (it allows to make “symmetry-transformations” around the original background see B-F) and this is independent of whether the perturbative implementation has a finite number of parameters or not ((no)nrenormalizable). The recent perception that massless finite helicity representations have natural string-localized fields with excellent short distance behavior
http://br.arxiv.org/abs/math-ph/0511042
generates new hope that the last word on finite versus infinite parameters has not yet been spoken.
A similar tendency (a return of reconciliation of gravity with QFT) is evident in
http://br.arxiv.org/abs/gr-qc/0610018
the problem in that approach is how one can reconcile the asymptotic safety requirement with the continued validity of background independence for short distances (or whether one should give up b. i. for s.d.)
Finally I would like to express my wholehearted sympathy with Nakanishi’s recent critical view on these problems
http://br.arxiv.org/abs/hep-th/0610090
His postulate: In the ultimate theory, any concept of classical physics must not”appear logically prior to its quantum-theoretical construction” is nothing else than Pascual Jordan’s plea to walk (in QFT) without classical crutches which is also the Leitmotiv of AQFT.
In fact the characterization of QFT in terms of relative modular positioning of a finite number of copies of a “monade” in the last section of my essay (not a metaphoric picture but a rigorous theorem!!) is a nice illustration that even the last vestiges of classical thinking can be removed from QFT.
I do not understand his distinction between on- and off- shell supersymmetry but I am in complete agreement with his emphasis on un-naturalness of this concept (for me it is even too rigid for finding any beauty in it). I don’t think that SUSY can be broken in any meaningful sense of this word (it is much too rigid for that). Already in the most soft way of symmetry breaking (by bringing the system into contact with a heat bath) it collapses instead of suffering a spontaneous breaking
http://br.arxiv.org/abs/hep-th/9812179
Dear Peter Woit,
For your second-edition NEW (perhaps published after LHC results?)
have you considered
1- adding lots of pictures and diagrams, pictures of GUT, standard model particles, SUSY-breaking scenarios, Feynman diagrams, Kaluza Klein etc.? Pictures fo SM and then MSSM, picture of GUT SU(5), etc., A picture of how large a number 10^120 (for cc) and 10^500 (for vacua) is helpful in comparison to pictures and photos of deviations from observation QFT anomlous moment of electron, and GR on binary neutron stars, is. pictures of Higgs, pictures of Higgs triplets. picture of how string theory is supposed to make up the SM, and pictures on why this scenario is probably wrong.
pictures of W Z Y bosons and how Higgs is supposed to break them. Picture of Higgs self-energy and fine tuning.
2- have a chapter written by someone else (i.e Rovelli) on why strings fails as a theory of quantum gravity? (with pictures of course).
3- Whether KKLT is plausible or unphysical (with pictures on what these flux wrapping look like) along with pictures of epicycles.
4- A chapter first on the ethical responsibilities of scientists, the need for scientists to be skeptical, and printing colorful email and weblog responses from string theorists (i.e lubos, jaques, and possibly others) — For the reader’s entertainment and insight on what some string theorists fall from the idea of what a scientist should be. pictures of the major string theorists might be helpful. pictures of obnoxious string theorists who write obnoxious emails also helpful.
5- FAQ chapter of standard string theorist objections and your counter-arguments with pictures, if applicable. Jaques Distler for example, compares string theory vaccua to infinite QFT’S.
6- Summary of predictions of string theory (or lack thereof) perhaps in table format.
Such a book could reach a wider, popular audience.
Dear David,
you said:
“I will read those papers carefully.
Regarding notation: I was calling it algebraic holography to distinguish it from gravitational holography. I was not trying to make anything else implied. I was trying to separate the objects of the discussion to avoid confusions.”
Take your time because the conceptual and mathematical complexity is not lesser than in ST (and if I would take notice of the existence of ST for the first time, it would take me much more than a week only to get a rough impression of what it is about).
My problem with ‘t Hoofts “gravitational holography” is that I simply don’t understand it (too vague). The post ‘t Hoofts paper which comes my mathematically and conceptually very precise form of (Minkowski and CST) holography close is one of Susskind’s paper where he connects it with the so-called “lightcone quantization” without anything gravitational. The problem is that this was not even done correctly in the case of free fields (there he is in the company of all the lightcone quantizers). But whereas in that special case there really exist a linear relation between the free field in the bulk and its appropriately defined lightfront restriction, this ceases to be the case and I do not know any other way than to convert the bulk field into the operator algebra it generates (also generated by all its composites) and to carry out the holographic projection with this algebra. At the end you may express the net of algebras indexed by the natural compact regions on the lightfront (which are nonlocal relative to those in the bulk) again in terms of one of its generating fields (these are the fields which obey the transverse extended chiral field relations similar to W algebras). The conceptual and mathematical structure is explained (as well as I am presently able to) in
http://br.arxiv.org/abs/hep-th/0511291
whereas the technology has been done in the first part of this 2-part paper. If you look into it you will see the subtlety of statements like the degree of freedoms “live” on the horizon or in the bulk.
Compared to the null-surface situation the AdS–CFT case is easier (from a conceptual point of view) because that relative nonlocal behavior is absent. In that case the AdS—>CFT direction can be done directly in terms of local fields. For those CFT which come from a “standard” (this can be made very precise) AdS the inversion in terms of pointlike fields is tricky but still can be done (and the result is a nonstandard CFT), whereas the inverse CFT—>AdS for a standard CFT is best done in terms of algebras. It is very instructive to start with a conformal free field. Then you get one of those “hollow” nonstandard AdS theories (see the the paper of Duetsch-Rehren and the lecture notes of Rehren).
Bert
I always considered the Kaluza-Klein idea to be incompatible with the structure of internal/external symmetries (external is short hand for spacetime) of QFT. The reason why younger physicists do not see any problem with K-K I ascribe to the fact that the kind of deeper knowledge about particle physics has already been eroded by decades of string-caused metaphoric thinking. I feel very comfortable in the company of Noboru Nakanishi who says in his recent article “Spacetime in the Ultimate Theory”:
“It is the cheapest idea to extend the spacetime to the one having a dimensionality higher
than 4. Nevertheless, recently, it has become quite fashionable to investigate the theory of
extra dimensions. The grounds for considering it seem to be the excuse that any possibility
is worth investigating as far as it is not completely denied by experimental evidences and
the expectation that it might be possible to resolve the hierarchy problem stated in [A] by
introducing new parameters in the extra-dimension space. It is quite disgusting to revive
the old Kaluza-Klein theory without any essentially new idea for resolving the fundamental
problem of how to expel the extra dimensions from the physical world. Furthermore, the
higher-dimensional theory makes ultraviolet-divergence difficulty out of control; the extradimension
people merely hope, without showing its ground, that the divergence problem
might be resolved by a non-perturbative treatment.
The dimensionality of the spacetime where we live is undoubtedly 4. There is no other
observation more manifest than this fact. The extra dimensions, whose number is denoted
by , are qualitatively different from the physical spacetime dimensions from the outset.
Recently, the superstring people have proposed the hypothesis that all fields other than the
gravity are confined to a soliton-like (according to their claim) object called the “-brane”,
but it would be quite difficult to formulate such an idea within the framework of the (4+)-
dimensional quantum field theory. A theory is worth being called a (4+)-dimensional one
if and only if its fundamental action is (4+)-dimensionally symmetric. But such a theory
remains (4 + )-dimensionally symmetric unless one breaks it artificially. In order to make
the -dimensional extra space invisible, the extra-dimension people are forced to make it
round into a tiny one by hand. This procedure implies that they are actually considering
the 4-dimensional spacetime accompanied with an -dimensional internal space. If so, they
should honestly claim that the extra dimensions are internal. Then there is no logical basis
for adopting a (4 +)-dimensionally symmetric action. It is quite non-scientific to pretend
as if such an action were a privileged one according to the symmetry principle.
There may be the objection that the extra dimensions are made round not by hand but
“spontaneously”. Certainly, there is no “proof” of the no-go theorem stating that the desired
spontaneous compactification can never take place. But if they assert the possibility of such
compactification, the responsibility of verifying it must be attributed to those who assert
it. That is, the extra-dimension people should construct at least one model in which the
spontaneous compactification of the extra dimensions takes place in a natural way. I cannot
believe that such a model can be constructed without greatly changing the framework of the
conventional quantum field theory, because the situation encountered here is qualitatively
different from the ordinary spontaneous breakdown of symmetry.
In fact this is corroborated by the most profound results about internal symmetries from AQFT. In that conceptual framework of QFT the relation of inner symmetries (including statistics) with the spacetime localization structure arises from the representation theory of local observables (bosonic by definition). In 4-dimensional theories this leads to the field algebra with a compact group symmetry (the structural DR theorem admits in principle any compact group). Supersymmetry is the extremely artificial (and unstable under total collapse, not symmetry-breaking) situation in which the observable algebra is fine-tuned and amalgamated together with one of its fermionic representations.
This representation theoretical origin of internal symmetries is incompatible with “little curled up spacetime dimensions”. Such a picture is only possible in a classical setting i.e. one has to do it there and then quantize. This is in complete agreement with what Noboru Nakanishi (and I think every particle physicist who made his career before the great string theory sell-out) says.
I have not yet read the paper or any of the comments in this post, but I must say I’m excited to hear this news. Bert’s other paper earlier in the year was very enlightening for me as an outsider and deals with things that to the uniniated such as myself seem to not be given due scrutiny. Can’t wait to read it.
Bert says:
I disagree with this postulate. The following is the reasoning: What is quantum mechanics? Is it something which tells us what the Universe is? Or is it a prescription for saying what the probability of getting experimental results is?
The idea that we need to get rid of “classical crutches” supposes the former. The overwhelming consensus of the physicists who took the time to think carefully about the issues involved (the Copenhagen school) is that the latter is the case. Everybody can have his own opinion of course, and the people who do not carefully go through the arguments which lead to the Copenhagen interpretation will probably not arrive at the same conclusion. The people who like to go with their “gut feeling” will choose the other conclusion, because it is nicer to think that the mathematics we use describes the Universe itself rather than encapsulating our knowledge of the statistics of experimental results. But the only reason I have ever heard for dismissing the idea that the mathematics describes statistics of measurement results is “gut feeling”, and perhaps an expression of contempt for careful thought.
In fact, in answer to the question of where the confusion in modern physics comes from, it seems clear to me (and I think Lee Smolin, among others, agrees with me) that it starts with quantum mechanics, and after quantum mechanics nobody knows what’s real and what isn’t. That’s when metaphors replace literal statements. And we have aggressive insistence from various people that there’s nothing to be confused about and everything is clear, but different people are selling different interpretations and they disagree with each other violently and dismiss each other’s views as not worth considering.
Question: Does the string theory project implicitly assume that the Copenhagen interpretation is wrong? Remember that Copenhagen is still the official interpretation of mainstream physics.
So, we have a clear and unambiguous interpretation of quantum mechanics as a formula for predicting results of measurements. But this needs the classical concept (or “crutch”) of a measurement and its result. People propose to get rid of the measurements and their results and what do they have left? Just a Hilbert space and an element of it (the hypothetical “wave function of the Universe”), and no way to relate it to observed phenomena (stories about unobservable parallel worlds are supposed to make up for it), the same problem that string theory suffers from.
Egbert
there is a fundamental misunderstanding here; what Jordan had in mind and what I mean has nothing to do with Bohr’s (and the Kopenhagen school) emphasis that our language for interpretating QM must be the classical one which relates to our perception of the material world. What was at issue is the classical parallelism called (Lagrangian) quantization. QT is more fundamental than classical theory and quantization is a very limited and entirely metaphoric way to access QT. The deep conceptual insight is to understand how the classical world re-emerges from the quantum setting, but this is the opposite of quantization.
Egbert
there is a nice old bom mot from the mathematician and mathematical physicists Ed Nelson:
(first) quantization is a mystery but second quantization (without interactions) is a functor.
mystery=metaphor
Bert, is what Jordan had in mind by any chance found in Jordan Algebra? John Baez in a coversation with Tony Smith once said that what you want is something that is both a Lie Algebra and a Jordan Algebra. Very loosely I think this could mean Lie Algebra is the classical-like thing and Jordan Algebra is the quantum-like thing. The relationship between Lie Algebra and Jordan Algebra might then be what you called a deep conceptual insight. Lee Smolin wrote a nice paper on the relationship between Jordan Algebra and String Theory.
http://xxx.lanl.gov/PS_cache/hep-th/pdf/0104/0104050.pdf
One of the references in this paper is a bosonic M-theory paper by Horowitz and Susskind. If only Susskind would work more on this than the Landscape!
John Gonsowski
certainly not. The plea for a new access to QFT without “classical crutches” is from 1929 and as far as I remeber the propsal about Jordan algebras is from 1934/35 (the best is the joint work with von Neumann and Wigner). Jordan algebras play an important role in generalizing QM (in particular to get a good understanding of the relation algebra—states, see the book by Bratteli and Robinson). But I think there is a theorem that (under very general condition) each infinite dimensional Jordan Algebra is a von Neumann algebra (see also a paper by Jochum). The 1929 Jordan plea goes into a quite different direction namely to liberate QFT freom those nasty (intrinsically singular) “field-coordinatizations” in analogy to the liberation of geometry from coordinates in modern Diff. geometry. This has been achieved in AQFT, in fact AQFT came into beiing precisely as a result of removing the undesirable features of the (Borchers) singular composite field classes (i.e. to have instead of infinitely many field coordinates just one object: the net of local algebras (which any one of them generates)
If my apprehensions that years of co-existence with stringy metaphors breeds ideological prejudices still needed confirmation, the reader can find it now in the writings of Distler and Motl. (see also remarks in my lecture notes which aooeared on Mondays hep-th posting)
Distler: “The troubling aspect is the totemic power of the word “Theorem,” and its ability (in the minds of some) to trump sound physical arguments and abundant calculational evidence.” Have string theorists (after their sociologically successful magic trick three decades ago to liberate themselves from the bonds of observational control) now also abandoned any commitment to mathematical checks because they feel threatened by Rehren’s theorem?
“…were it not for the peculiar amplifying nature of the internet that has, apparently, given these ideas a certain currency among impressionable young students.”
Perhaps we have to go back to Socrates and his contemporaries; what about threatening Rehren with the cup of hemlock (after all one of the opponents of rigorous theorems is also a specialist in death threats)?
“when we met in person, he seemed like a very nice guy”,
does Distler expect that opponents of string ideas look like teeth-grinding monsters?
Putting the re-hashing of a non-continuous quantization of the Weyl algebra (which in the beginnings of QM was invented to show that not every representation of it allows a return to the Heisenberg commutation relation) on par with a recent deep AdS—QFT holography theorem can only be done by somebody who does not understand the theorem or willfully wants to exorcise it because goes it may cross the path of his holy grail; in the present case the motivation seems to be a mixture of the two.
The problem why Rehren has these difficulties with the string community is that they apparently are not aware that holography is not a manifestation of gravity (it can be derived with or without gravity). They do not seem to know that there is now a generalization of QFT which incorporates the local covariance (diffeomorphism covariance) principle and which also shows that a perturbative treatment of quantum gravity is consistent with background independence (if the QFT obeys the quantum Einstein-Hilbert equations). It would be interesting to say something more about these recent results on this on this blog (in case of interest) since this new insight destroys the mantra of ST and LQG that QFT and gravity are not compatible.
What’s the difference between “diffeomorphism covariance” and “diffeomorphism invariance,” and which is one the correct notion to apply in quantum gravity?
Bert, sorry, but this case I fail to see what’s wrong with what Distler/Motl say. In physics, a theorem can fail not only because it is technically wrong, but also because the axioms are wrong. E.g., a century ago people rigorously proved that Bohr’s model of the atom was wrong – according to classical mechanics, the electrons will lose energy an eventually fall into the nucleus. The problem was that the theorem was wrong because the axioms of classical mechanics do not apply to the hydrogen atom.
Similarly, it is possible that there are some exotic systems that obey the axioms of QM in a generalized sense, but that does not mean that such systems are realized in nature. It seems to me that LQG’s failure to reproduce the harmonic oscillator as we know it is a show-stopper, plain and simple. There is hardly any system better studied that the oscillator, neither theoretically nor experimentally. Convincing physicists that there is a new kind of quantization which gives different result for the oscillator is not going to happen.
About Rehren duality, I really have no opinion, because I don’t understand it. However, if what Motl write is correct, that a bulk field psi(x,y,z) is dual to a boundary field psi_z(x,y), then it seems pretty trivial to me. Besides, I think that the value of dualities are highly overrated. A duality is only interesting if one side is physical and the other is tractable, something which seems to be the case neither for Maldacena nor Rehren duality.
Rather than giving up established knowledge, progress is obtained by finding the loopholes. The loophole relevant to quantum gravity can be found here. Note how Robert reluctanty agrees with me, and how Motl and Distler refrain from explaining that I am an incompentent moron who does not understand the difference between a gauge and a global symmetry, which they undoubtedly would have done if I had given them a chance.
In the unlikely case that somebody cares, I did point out to Lee Smolin that the LOST theorem might be wrong because its axioms are wrong here, before Distler and Motl did so.
Anon
Diffeomorphism covariance (or simply local covariance) is a concept that Einstein introduced. In special relativity, even though Newton’s absolute space-time has been abandoned, it was still meaningful to talk about events as spacetime points in a given background.
In general relativity spacetime points however loose this apriori meaning because the principle of general covariance forces one to consider a point as belonging simultaneously to many different spacetimes (an unusually abstract idea which most students of GR became aware only very late). The reason for this abstraction is as follows. Imagine that you have a classical system of electromagnetic field strength and metric tensor satisfying together the Maxwell-Einstein equations. Suppose these fields are known prior to some spacelike surface Σ then, indeed, without conditions for the coordinatization of future points one has no Cauchy problem. As is well known, the Einstein equations give four constraints for the metric field and its normal derivative on the surface Σ and only 6 “dynamical” equations for the 10 quantities gμv. If the observer establishes the
labelling of future points of M (coordinatization) by means of conventions using only Fμv and gμv, then the mentioned diffeomorphism will have no effect on his observations. The “change of the physical situation” is exactly compensated by his
change of the labelling of the points. The field equations together with such coordinate conditions provide a deterministic scheme.
The active interpretation of general covariance demands therefore that we imagine the possibility of decoupling the labelling of (future) points of the manifold from the prevailing configurations of
fields which obey a closed system of intrinsic field equations. The upshot of this is that a point which was contained in a spacetime region is as well belonging to any other spacetime region which is isometric to it. In other words if you live in a world in which only a (causally complete) part is physically accessible then you cannot distinguish this situation from any other world which has a patch which is isometric to the original region. This is a consequence of the active interpretation of transformations (i.e. diffeomorphisms and not coordinate transformations) and therefore comparisons with gauge theories (where one was forced to introduce to introduce redundant descriptions) may be misleading (those do not have an active interpretation).
The phantastic progress in QFT in CST was the recognition that with a more abstract notion of what constitutes a QFT (a new functorial concept which contains the old one as a special case) you can implement local covariance in QFT in CST
http://br.arxiv.org/abs/gr-qc/0603079
(look also at the literature cited therein)
This is after Einstein and black holes the third great step in gravity!
If in addition you quantize gravity (say perturbatively) the already established local covariance will automatically pass to background independence i.e. the change of one background to another one becomes a symmetry transformation in the full quantum theory (the argument on page 120). The problem whether there are other ways of quantizing which make QG a theory with a finite number of parameters (the standard way leads to an ever increasing number with increasing perturbative order) is not entering here because any perturbative approach will lead to a perturbative fulfillment of the Einstein-Hilbert like operator equation and hence the B-F argument applies.
Hence the claim that QT and gravity are not compatible has finally been shown incorrect. This also is relevant to Lee Smolin who seems to have internalized this mantra during his years as a ST.
I have bothered Peter to have a special blog on this important matter which changes the rules of the game in town, but he is immersed in combating the ST backlash via embedded journalists. What criticism can be stronger than this invalidation of the ST mantra?
Thomas Larsson
I will return to your question later on. Meanwhile you may read what I wrote for Anon, because the Maldacena issue is not independent of these new developments in QFT.
Thomas Larsson
the short answer to your remark is the following question:
Is the starting point of Maldacena (not what he actually argues but how he wants his conjecture to be understood) a conformal field theory (even one having a Lagrangian description: SUYM) a 4-dim CFT, yes or no?
If the answer is yes then Rehren’s theorem applies, he does not have any other assumptions. But then how can M be correct? If the answer is no than Maldecena may be correct but the boundary value he imagines cannot be a CFT. I do not know whether the N->infinity limit is conformal, in fact I have never seen a proof that one obtains conformality for finite N. I think the only safe statement seem to be the vanishing of the beta function in lowest order. Lets for the sake of the argument assume that not only beta=0 but also conformality (stronger than beta=0). Then one would think that this property is maintained for N=infinity. Here one has to be a bit careful because that double limit (large ‘t Hooft and large color) is not a naive limit which maintains field theoretic properties. But to imagine that bluff!!, suddenly conformality is lost in the limit is a bit far-fetched.
As Rehren has pointed out in his discussion with Distler (he stopped that discussion after it became obvious that there was no point in a continuation) that “restriction” and what they call”duality” in that discussion is the same (this to me very surprising and highly nontrivial statement was shown by Duetsch and Rehren).
I think that the origin of this misunderstanding of Rehren’s work by ST is the way in which ‘t Hooft conceived “holography” as a mysterious property of gravity. This picture (the metaphoric part of Distler’s discussion) is incorrect, holography is defined with or without gravity. In addition this picture would contradict the unity achieved via that fantastic extension of QFT which I sketched in my comment to anon.
The whole situation is very tragic because it shows that with the market force and embedded journalists the survival of individual researchers against corporate groups is endangered, at this point Lee is 100% right. This weekend I have watched the KITP glee club with the embedded cantor. While I was listening I laughed the lung out of my body. But as every indulgence breeds remorse I thought afterwards in bed, my God how could this happen to a once proud and purposeful science.
All the tangible progress (including the work mentioned before) has been done by individual researchers and nothing has come from those globalized communities. Let them fight it out, while we move on.
“comparisons with gauge theories (where one was forced to introduce to introduce redundant descriptions) may be misleading”
So you’re saying the 10 components ( d(d+1)/2 components in d dimensions) of the metric tensor are not a “redundant description” along the lines of the 4 components ( d components) of the vector potential of electromagnetism?
Anon
No I am not saying that; if you work with pointlike metric tensor quantum fields you presumably have to use some BRST ghosts in order to reduce to the physical cohomology even literally speaking the theory is not a gauge theory. I understand that such a formalism is presently being worked out by Brunetti and Fredenhagen. I am looking at this problem (together with Jens Mund and Jakob Yngvason) without using ghosts by setting up a perturbation theory with our string-localized metric potentials.
What I had in mind in that phrase was that in the classical theory as well as in QFT in CST the local covariance principle forces one to interpret diffeomorphisms in the active sense (this is what they mean to mathematicians) and not as a change of coordinates whereas the gauge transformations in electrodynamics are purely passive.