This evening a very interesting paper appeared on the arXiv, entitled Instantons Beyond Topological Theory I by E. Frenkel, Losev and Nekrasov. The authors are studying theories with a topological sector (supersymmetric quantum mechanics and 2d sigma models on a Kahler manifold, N=2 supersymmetric YM in 4d), but are interested in sectors of the theories that are not purely topological. I’m looking forward to reading the paper over the next few days, but it is a bit daunting. This paper is nearly 100 pages long, and it is only part I of three parts, and actually just the simplest part, that involving quantum mechanics.
HEPAP is meeting today and tomorrow, here’s the agenda. From the slides of the talk about NASA, the budget situation there for fundamental science missions doesn’t look good, and there is discussion of the upcoming NRC committee charged with figuring out which of the “Beyond Einstein” missions to allow to go forward. At Dynamics of Cats, Stein Sigurosson has been writing about this in terms of the missions being sent to Thunderdome, only one to emerge alive.
Slides from the talks last month at the conference in honor of Nigel Hitchin’s 60th birthday are available.
Joe Lykken has a nice review article about the standard model, in which he notes:
There is only one diagonal Yukawa coupling that is of order one, and that is the top quark Yukawa. But even this case is mysterious. The top Yukawa is not really of order one: it is equal to one! For example, using the 2005 combined Tevatron value for the pole mass of the top quark, the corresponding Yukawa coupling is 0.99 +/- 0.01. The entire particle physics community has chosen (so far) to regard this fact as a 1 per cent coincidence. I should point out that similar percent level equalities, e.g. supersymmetric gauge coupling unification or the ratio of the total mass-energy density of the universe to the critical density, have spawned huge theoretical frameworks bolstered by thousands of papers.
Difference is that, as far as I know, nobody has an idea why this Yukawa coupling should be one. Maybe this is a big clue…
Over at Backreaction, there’s an excellent posting about Does String Theory Explain Heavy Ion Physics?, one of the very few places to find a non-overhyped discussion of this topic.
Davide Castelvecchi has a well-done review of my book at his sciencewriter.org web-site.
At this week’s physics colloquium at Penn, Andre Brown reports that Robert Cahn emphasized that “half the particles needed for supersymmetry have already been discovered.” He also recalled a quote from another colloquium about supersymmetry: “Supersymmetry has stood the test of time. There is no evidence for supersymmetry.”
Update: A couple people have pointed out the following rather accurate cartoon.
Concerning Beyond Einstein: Judging from the crowd Goddard sent to HEAD, Constellation-X will win. As Harvey Tananbaum pointed out:
1) CON-X is considered first priority after JWST
2) CON-X and LISA are approved programmes.
In his Saturday talk, Roger Blandford urged us to attack fundamental problems directly instead of assumption-fitting model building. He described current theory as epicycles and avoided mentioning “dark energy.”
The COSMO 2006 Meeting a week before in Lake Tahoe was more fertile ground for JDEM support. The SNAP team sent just one speaker, and the poor woman was asking around for a ride because she had no way of getting back to Berkeley. Is she still there? Is SNAP running low on petty cash? Watching the Blue Angels was the most fun of the week.
Concerning the reduced budget etc … does anybody have some insight into why the US gov is determined to spend less and less on basic science? It all seems quite weird.
Compared to other types of investment, it seems like scientists are a rather cheap resource and the rewards of a larger scientific community are so great.
Even in the face of fears of greater competition from China and India and almost daily fretting about outsourcing of jobs, absolutely nothing seems to be done and day by day, less and less is spent … year after year of decreasing budgets …
Is there something I am missing?
TheGraduate,
The US government actually is increasing the budget for fundamental physics research. NASA seems to be a different story, with all the manned space flight issues.
At the KITP (then the ITP), someone from the NSF once gave a talk on science budget issues, and they showed a graph that demonstrated how entitlements were squeezing everything else out of the budget. You didn’t have to project the trends very far forward to get to a point where there was no money for science.
King Ray:
You said “they showed a graph that demonstrated how entitlements were squeezing everything else out of the budget”
What kind of entitlements did he mean, like health benefits, sabaticals and tenure?
Peter,
When you say it is increasing, do you mean it’s increasing this year or it has always been increasing and does this increase still hold up if we correct for inflation?
I hope it actually is increasing. That would be great.
Peter said “… Joe Lykken has a nice review article about the standard model [ at hep-ph/0609274 ], in which he notes: … The top Yukawa … is equal to one! …”.
Peter goes on to say: “… as far as I know, nobody has an idea why this Yukawa coupling should be one. …”.
One natural reason for the T-quark Yukawa coupling to be “equal to one” would be for the Higgs to be a T-quark condensate, as in a modified Nambu-Jona-Lasinio ( NJL ) model such as that described in hep-ph/0311165 Michio Hashimoto, Masaharu Tanabashi, and Koichi Yamawaki.
In that paper, they say “… the scalar bound state of tbar-t plays the role of the Higgs boson in the SM …”.
To avoid some of the problems of a simple NJL model, they consider Kaluza-Klein type “TeV-scale extra dimension[s]” and “… found that the bulk QCD coupling can … become suffciently large to trigger the top condensation for … D = 8 …[and]… predict the top quark mass
mt = 172 – 175 GeV for D = 8 …”.
Since their result is close to an observed value of a T-quark mass peak in Fermilab data, and
since their work is consistent with 8-dimensional structures in my physics model, and
since related structures seem to me to be related to some Fermilab experimental data in the ranges of mt around 130 GeV and around 225 GeV that seem to me to be important,
I described in a talk I gave at the April 2005 Tampa APS DPF meeting the above results of hep-ph/0311165 by Michio Hashimoto, Masaharu Tanabashi, and Koichi Yamawaki.
Joe Lykken chaired the session at which I spoke, and he seemed interested while I was giving the 10-minute talk. At the end of the talk he told me that he would take the ideas in my presentation back to Fermilab, and see if the people there had any interest in working on such approaches.
In the year that has followed, no interest has been expressed by Fermilab, and I see that the work of Hashimoto, Tanabashi, and Yamawaki (who are from Pusan, Tohuku, and Nagoya) is not mentioned in Joe Lykken’s paper at hep-ph/0609274, which is a subject of this blog entry by Peter.
I am disappointed and puzzled at the lack of interest in such an approach with obviously realistic contact with experimental results. Sometimes I think that maybe my status as a blacklisted “moronic crackpot” may discourage interest, and sometimes I think that maybe there really is a bias in the USA against the Nagoya group (after all, Kobayashi and Maskawa have yet to get a Nobel, even though it has long been obvious that they deserve it)).
Tony Smith
http://www.valdostamuseum.org/hamsmith/
PS – Since the DPF meeting this year (around Halloween) is a joint meeting in Hawaii of the APS DPF and the JPS, and is designated “Joint Meeting of Pacific Region Particle Physics Communities”, I looked at the list of participants at http://www.dpf2006.org/DPF06%20Participants.pdf
to see whether MIchio Hashimoto, Masaharu Tanabashi, and Koichi Yamawaki might be participating.
To my regret, I did not see any of them listed (the list was dated 10-12-2006) as participants.
I think with the issue of string theory, it is best to look at things the way a banker would. When one goes to a banker looking for money, he looks at your financial history, if in the past you have not made money, it will be difficult to get more money in the present. It is evidence based decision making.
I think while we all tend to sympathize more with the person in search of funds, we want someone like the banker in charge of our children’s college fund. Last thing you want to hear is that the banker put everything on something with no track record!
I think its pretty easy to get wrapped up in present details about how it will ALL BE DIFFERENT FROM NOW ON. (That’s how people talk when they are all caught up in any activity! It doesn’t really mean anything that people feel that way.)
What matters is waiting for a potential project to build up a record before funding in large amounts. Of course small amounts are okay. Now, the other thing to think about is if concrete measures show that two approachs are on equal footing then they should both be funded with equal probabilty (and with small amounts!).
I liked Smolin’s discussion of venture capitalism. I think he gets it.
The top Yukawa coupling is convention dependent and runs with
energy. Who cares if it is exactly one in some conventions at some
energy scale? The other quantities that Lykken mentions people
working are not of this type.
TheGraduate,
In HEP US funding has been flat or decreasing for quite a few years, but is supposed to increase significantly for the coming year and for the next few years. For some reason, Bush made physics research a central part of his “American Competitiveness Initiative”.
Capitalist Wr, the idea about the coupling being a convention emanates from the ideology of GUT, that says that every prediction must be imposed at the GUT scale and then run down to the electroweak scale (or even downto the IR limit?).
What we have here is that there is low energy relationship between Fermi constant (which sets the electroweak vacuum) and the top quark mass (which relates to the electroweak vacuum via its coupling constant).
For all its success, it’s good to be reminded of just how balled up and complex the SM really is, and how critically tuned to the Higgs mass it is. That has always seemed to me to be odd.
-drl
Peter said “Joe Lykken has a nice review article about the standard model”.
I greatly enjoyed Lykken’s article “Standard Model: Alchemy and Astrology,” especially his statement:
“A decade from now, we will look back on our current understanding of the Standard Model and be amused at its lack of sophistication.”
Peter, I thought you liked the standard model and I was surprised that you would provide a link to an article which compares the Standard Model to Alchemy and Astrology!
Thomas,
The SM occupies a strange place in physics history. The basic idea is gauge theory – which in itself, requires long-distance interactions. To make the SM work, you have to remove the very thing that characterizes the main idea. No other real theory is like that. In other theories the main idea assumes a prominent role. When this issue is resolved, the Higgs mechanism will indeed look outmoded.
One should not slight either alchemy or astrology. The former lead to psychology, and the latter, to astronomy.
-drl
Instantons Beyond Topological Theory I
This paper is just another exhibit of a misconceived relation between mathematics and physics which presents impressive mathematical results using metaphoric particle physics terminology. The potential harm of just papers is exclusively on the side of physics (with newcomers of QFT who are still struggling with its conceptual basis). The physics side of this much heralded new age between math. and phys. which ever since Atiyah-Witten (for lack of a better name for this math. phys. trend) has been metaphoric on the side of QFT (its relation to QM was more balanced than that to local quantum physics) left particle physics empty-handed. Where at the beginning it had the positive effect for serving as a kind of innovative catalyzer for new mathematics, it now flows back emanating from mathematicians who obviously think they are doing mathematically rigorous QFT whereas they are using physical metaphors to present excellent mathematical results. QFT is unitarity (positivity), causal locality and stability properties (energy positivity, KMS thermal states) and its hallmark which separates it from QM is interaction-caused vacuum polarization. Free field like constructions whose only physical nontrivial aspect is due to using non Lorentzian living space for fields may be mathematically interesting but they do not help for a mathematically controllable construction of interacting quantum fields.
The Standard Model: Alchemy and Astrology
The main source for the presence of Alchemy and Astrology in the SM is the unfortunate (but apparently ineradicable) metaphoric presentation of the Schwinger-Higgs mechanism of charge-screening (the abominable “fattening of the photon”). A slightly less metaphoric way consists in starting with pointlike massive free vectormesons:
http://br.arxiv.org/abs/hep-th/9906089
In order to remove the last metaphoric vestiges one has to substitute the BRST gauge formalism by a different description of massive vectormesons in terms of a string-localized field with a very nice short distance behavior (without change of physical content). I have described this in the last section of my essay (see the Samizdat weblog) but did not find the time to elaborate it.
I forgot to explain why the Schwinger-Higgs mechanism has nothing to do with symmetry-breaking (already known through Elitzur’s old paper) but rather describes screening. This becomes obvious if one takes the decoupling limit for the Higgs particle (can be done perturbatively) which leads to charge liberation (the opposite side of the medal).
The point is, one starts from Fermi Constant, as measured eg in muon beta decay, G_F=1.16637(1) 10-5 Gev-2, and from this one extracts an “EW vacuum”, sqrt(G_F sqrt(2)) = 246.221. You can see this quantitiy in the standard report. The Yukawa coupling is calculated from a quantity differing by sqrt(2) and that we also call the “EW vacuum”. It is thus 246.221 sqrt(2) = 174.104(1) GeV. Both quantities are used in the standard model because the later is more simple when attaching to fermions, but the former gets a nicer expresion against the mass of W. Nicer only in the sense that people is used to it.
So ok, we have 174.104(1) Now go again to the pdg and take the values of the top mass, either directly measured, 174.2+-3.3, or from the SM global fit, 172.3+10.2-7.6. Ok, from this global (conservative) fit you get only a quotient .9896+0.059-0.044. But from the *measurement* you get 1.0005 +- 0.019
Dorigo has also tryed to champion on this regularity. What is worse is when theoretist say “it is of order one”. I mean, if you think it is just a casual thing, you should not mention it ever; it you think it is not casual, it is not of order one, but it is is exactly one plus, if you wish, corrections of about order alpha (or your favorite coupling constant here). What happens is that a log of GUT, SusyGUT and higher models (including some from the string with “free fermions”) get to relate the scale of EW breaking with the mass of the Top (hey, even Connes’s models do it), and the people presenting results find more convenient to think on “order one” from the theory than to face the experimental result. You can argue that the experiment still allows a 3% deviation easily, but even so, we have already not a o(1) but a o(0.1) gained, and with a huge probability of being o(0.01)
Hmm sorry, it is 1/sqrt(G_F sqrt(2)) (as obvious from the units).
So, Sqrt(2) is supposed to play a fundamental role? What if you needed Pi Sqrt(3) to get the ratio to be 1? Would that be as exciting? As I said before, it is convention dependent. Putting in the Sqrt(2) just cleans up some formulae. It has nothing to do with GUTS. And of course it runs, so at higher energies this relation would not be true.
Peter,
It’s really entertaining to read your blog when I have a minute or two to kill. I have no idea what the purpose of the comment section is but it definitely contributes to certain individuals calling you ‘crackpot’, ‘crank’, etc. Please see Bert Schroer’s comment. If I as an outside observer see such a comment on a whatever blog I — no matter how impartial, unbiased, etc I am — would certainly conclude that this blog is a gathering spot of leisure crackpots.
Sorry to bring bad news but you would do yourself a favour if you would simply delete crackpot comments instead of contributing to publishing them and afterwords complain that people accuse you of the exact thing you actually do: contribute to publishing crackpotism.
Best,
Tim
Tim,
This is a real problem, but since one person’s “crackpotism” is another person’s serious scientific idea, I’d prefer to describe it as a problem of too much noise. All physics blogs that I know of that attract a significant number of comments have to struggle with this. It’s frankly a huge pain in the ass: how would you like to spend a significant amount of your time examining nearly 50 comments a day, trying to figure out what to do with them, and fielding outraged e-mail from people who feel that something they took a lot of trouble to write has been deleted?
Partly to keep this from completely taking over my life, I’ve tended to adopt a policy of erring on the side of not deleting comments. Undoubtedly this would be a better blog if I put more effort into moderating things and keeping the noise level down. But one thing I should point out to you, is that, from what I recall, you submit a significant number of comments that are non-substantive and off topic, definitely adding to the noise level here. If I do find time to be more aggressive about deleting comments, you might find many if not most of yours not appearing.
And please, this is off-topic. I’ll delete any more comments here about this. Stick to discussing what is in the postings. If you have a brilliant idea about what I can do to reduce the noise level without having to spend a lot more time on it, send it to me via e-mail.
CW, I do not know that to do of your last comment. Initially it seemed to me the typical damage from the [misinterpretation of, if you wish] doctrine of effective theories: As the Langrangian of Fermi beta decay is not the real thing, why to bother to learn it? And for the same token, as the formalism of the standard model is not the real thing, why to bother to learn it? On second reading, it seems that you are perfectly aware that these square roots come from the usual notation for that lagrangians and for the vector of electroweak breaking (the “higgs vacuum”, if you prefer), and that one puts them in advance to aliviate notation after normalisation of some vectors. But then you should know they come forcefully from these normalisations, and you should not to play with “pi sqrt(3)” as a pausible ratio (incidentally, pi is specially misleading, as you can not get a trascendent number as solution of an algebraic equation).
So, are you being serious in your question, or just rethoric?
Some old authors, by the way, never were happy with these squarerootings, and they used to say that the value of the electroweak vacuum is about 175 GeV
“This paper is just another exhibit of a misconceived relation between mathematics and physics which presents impressive mathematical results using metaphoric particle physics terminology.”
I don’t understand this criticism since the paper in question is about QM, which is mathematically well defined. QFT is mentioned, but is to be treated in the forthcoming sequels.
I’m sure I’ll learn much about QM by studying this paper. However I’ve never seen thermal KMS states teach anything about quantum statistical mechanics that wasn’t already known by traditional (although less mathematically rigorous techniques). Even the treatment of the thermal harmonic oscillator by Narnhofer and Thirring (Letters in Mathematical Physics, Vol 23 No 2 pg 133-142) seems to be similar to the coherent state treatment, but dressed up in fancy mathematical clothing. Do thermal KMS states teach us anything (physically interesting) about BEC or the Ising model that isn’t already widely known?
My comment is about the use of these methods in QFT. Let us see whether there will be anything including interactions (and the inexorable vacuum polarization going with interactions) coming from such methods. If there is, I of course will correct myself in public. I do not care about the spacetime dimension as long as it is at least 2. Oscillators do not impress me.
It is precisely that balance between mathematics and physical concepts which one finds in Thirring’s writing (and more generally in most of math. phys. coming out of Europe with the exception of Amsterdam and from string theory groups) which has been lost in that part of the particle physics community which takes its math from Atiyah and Witten.
By the way, there are meanwhile also quite nontrivial 2-dim. QFT which have been shown to be well-defined (most recently a very original AQFT method to show exitence for massive factorizing models has been discovered).
Another side to metaphorical thinking (perhaps?) is in the Jaffe/Quinn paper referenced in the n-Category Cafe:
http://golem.ph.utexas.edu/category/2006/10/wittgenstein_and_thurston_on_u.html>here
This is from 1993:
“When reliability of a literature is uncertain, the issue must be addressed. Often “rules of thumb” are used. For example, mathematicians presume that papers in physics journals are theoretical. This extends to a suspicion of mathematical-physics journals, where the papers are generally reliable (though with dangerous exceptions). Another widely applied criterion is that anything using functional integrals must be speculative. One of us has remarked on the difficulties this causes mathematicians trying to use solid instances of the technique [J]. These kinds of rules are unsatisfactory, as is the caveat emptor approach of letting each paper be judged for itself. Proponents of this latter view cite Witten’s papers as successful
examples. But a few instances can be handled; it is large numbers that are a disaster. Also, it is a common rule of thumb now to regard any paper by Witten as theoretical. This short-changes Witten’s work but illustrates the “better-safe-than-sorry” approach mainstream mathematics tends to take when questions arise.”
Not having a Science subscription, I can only get this teaser online, and wonder whether it relates to one of your recent references, and what it’s about:
Science 13 October 2006:
Vol. 314. no. 5797, p. 248
DOI: 10.1126/science.314.5797.248
News Focus
PARTICLE PHYSICS:
Tidy Triangle Dashes Hopes for Exotic Undiscovered Particles
Adrian Cho
Physicists have proved that their explanation of matter-antimatter asymmetry is essentially the whole story–even though many hoped the theory wouldn’t add up.
In my use of the attribute “metaphoric” I should have differentiated between a benign connotation and a malignant one. Clearly the use of the Higgs mechanism (the mass-dressing of the photon through the Higgs “condensate) and the gauge theoretic use of ghosts (which are not there in the beginning nor can they be tolerated in the final physical objects) are benign metaphors. Whether you compute using these metaphors or follow an autonomous path does not matter, you end up with the same renormalized expressions for the physical (gauge invariant in the metaphoric treatment, pointlike local in the autonomous derivation) quantities.
An example for a malignant metaphor is the statement that the Maldecena conjecture is an illustration of a mathematical theorem about the AdS—CFT correspondence. A pharaonic constructed erected by hundreds of people in thousands of publications cannot be undone by any rational argument. The only hope is that as a result of the unphysical nature of SUYM and AdS it will cease to circle over our heads and eventually become exclusively a topic for historians and sociologists of science.
For those among you who have not lost their sense of humor I attach a parody which Noboru Nakanishi (with his consent) wrote in 1986 i.e. at a time when skeptics as myself (and perhaps also Peter Woit) were still in a “lets give it a try” state of mind.
This is a faithful reproduction by LaTeX of a joke paper written in May, 1986 (unpublished).
COMMENTS ON THE SUPERSTRING SYNDROME
Noboru Nakanishi
Research Institute for Mathematical Sciences
Kyoto University, Kyoto 606, Japan
A recent epidemic among the Elementary Particle Theorists is the Superstring Syndrome, which causes the Kaluza-Klein symptoms. The pathogen is said to be much much smaller than any virus known and in shape of a string or a ring. Nothing certain is known about this virus, however, since nobody has ever seen it. There is a rumor that this virus has been cultivated under strict supervision of Drs. Green and Schwarz
By the way, it is said that these doctors are characters in the German-English translation of a famous novel by the distinguished writer Stendhal. It is also said that the translator is red-greeen blind.
and was released to outside by a researcher at the P-University (the author has chosen not to name him). This disease, unlike AIDS, does not have a tendency to prevail among homosexuals. In general, however, young and cheerful people are observed to be more susceptible to this disease. The infection occurs usually through mouth, as is true for the influenza. But since the infection occurs occasionally through eye, special precaution is necessary.
The String Syndrome had also been epidemic about ten and some years ago. At that time, the damage was a rather minor one, since it was not associated by the Kaluza-Klein symptoms. Eventually, the Yang-Mills was found to be an excellent remedy, and thus most of the patients were said to be completely cured. However, the current Superstring Syndrome is a much severe disease, for which the Yang-Mills may cause undesirable side-effects rather than remedy it. Adding further to the worries is the fact that brain might be affected. Under this disease, it is said that the patients fall in to a belief that something called “anomaly” is at the root of everything. In contrast to healthy people, who regard normal states as they are and then observe anomalous states as something deviating from them, the patients credit anomalous states and then observe normal states as deviations from them. Researchers of abnormal-psychology are therefore quite interested in this symptom.
The patients of the Superstring Syndrome believe in a Miracle. This is not a small miracle like the one in which Moses divided the Red-Sea into halves, but is the Great Miracle of the whole universe that the 10-dimensional space-time is divided into the 4-dimensional space-time and the 6-dimensional space. Although this separation has to be done completely, homogeneously and permanently throughout the whole universe, they cannot understand at all why it can be so. The patients just simply believe in it. It is said that a magic spell “Calabi-Yau” enables them to see clearly the extremely varied structures of the six-dimensional space. In fact, they must have experienced the wonderland stranger than that of Alice. In the very, very, very, very tiny world that is 20-orders as small as the scale of a nucleus, the classical geometry is claimed to hold to extreme accuracy. In that world, the mini-dragon Pyrgon must be striding in the vicinity of the Planck Length District wearing the top-mode of Anomaly-Free.
The patients can easily see this hallucination without LSD. They use new drugs called SST I and II. Although it is not yet known what exactly they are, it can be guessed from their pronunciations that they are similar to LSD. Since their safety is not confirmed by any clinical studies, it is advised that people should avoid their habitual use.
The trouble about the Superstring Syndrome is that, like drunks never acknowledging their drunkenness, the patients do not acknowledge their own abnormality. They regard the Kaluza-Klein symptoms as normal and lose the sight of the fact that this real world we live in is the genuine four-dimensional space-time. The present author is deeply concerned about the possibility of a disastrous situation in case an effective remedy is not invented in near future.
[Translated by Hideaki Aoyama. The original article is published in Soryushiron Kenkyu (Researches of Elementary-Particle Theory), Kyoto, 72 vol.6 (1986) 345, in Japanese.]
Bert, pretty tame compared to Warren Siegel’s magnum opus “The Everything of Theory”, about TOENAIL (theory of everything not appearing in laboratories 🙂
-drl
Joe Lykken writes that in 10 years we’ll look back and be amused at how unsophisticated the Standard Model of today is.
Is anybody amused by the lack of sophistication of the Standard Model circa 1996? What measurable quantities can we calculate now that we couldn’t calculate then?
Jonahtan, it is an article about the status of the unitary triangle after the recent measurements of B-meson mixings. Surely you can find more in the public reviews of the Particle Data Group.
Bert,
No one ever said that the Maldacena *conjecture* amounts to a *mathematical theorem* — If it were, how come everyone uses the word *conjecture*????
What more can people do than to keep on saying *conjecture* ????
It’s statements like these that are malignant and obfuscating and hurts the cause of any meaningful criticism of the current status of string theory as a physical theory which is far from being in good shape.
Please don’t confuse things. If anything, it surely hurts your cause.
Further, I find it unreasonable on your part to claim priority in discovering aspects of conformal field theory which you say is very physical (namely conformal blocks) before BPZ when it suits you, then criticize string theory for being a theory of free fields.
As I’m sure you know, string theory is based totally and completely on conformal quantum fields in 2 dimensions. Interactions come in via vertex operators, multi-genus Riemann surfaces, etc, etc. That’s the whole point.
Further, I don’t think that you have discovered conformal blocks (in the accepted definition of this concept) at all, since you didn’t know anything about Virasoro algebras, central extensions, and you definitely didn’t know about the minimal models.
There is another physicist who also likes to make such claims, but similarly, they are strictly unfair.
You all missed working at c smaller than 1.
MathPhys: It is far from the case that the Malcedena conjecture is always referred to as a conjecture. I was confused on this very issue until recently, simply because people are not that careful.
Walt,
Show me one serious string theorist who refers to it a mathematical theorem, and I’ll be very happy to admit being wrong.
Further, I don’t think that you have discovered conformal blocks (in the accepted definition of this concept) at all, since you didn’t know anything about Virasoro algebras, central extensions, and you definitely didn’t know about the minimal models.
Claiming that one can understand conformal symmetry in 2D without knowing about the Virasoro algebra is about as absurd as claiming that one can understand diffeomorphism symmetry without knowing about the analogous Virasoro-like extension of the spacetime diffeomorphism algebra. But then again, absurdity has never prevented people from making such claims.
I think they were dealing with 2D massive models, which they can now say are off critical deformations of conformal field theories.
But then again the proper treatment of the latter requires knowledge of the underlying deformed infinite dimensional algebra, something that was studied only after BPZ, and I’m not so sure is well understood to this day.
Aside from that, I’m afraid I will not believe a word of what you say about a central extension of spacetime diffeomorphism algebras until you write a paper on that, and it gets refereed and accepted for publication in a regular math journal.
The extension proportional to c_2 was published in
T.A. Larsson,”Central and non-central extensions of multi-graded Lie algebras”
J. Phys. A. 25 (1992) 1177–1184.
The extension proportional to c_1 was published in
S.E. Rao and R.V. Moody, “Vertex representations for $N$-toroidal Lie algebras and a generalization of the Virasoro algebra”
Comm. Math. Phys. 159 (1994) 239–264.
The paper is available online.
The representations were understood geometrically in
T.A. Larsson, “Extended diffeomorphism algebras and trajectories in jet space”
Comm. Math. Phys. 214 (2000) 469–491.
It is available online as math-ph/9810003.
It might be worth pointing out that Bob Moody is somewhat famous, e.g. for the codiscovery of something called Kac-Moody algebras back in 1968. But then again, maybe you don’t believe in Kac-Moody algebras neither.
Thomas,
Thanks for the references.
It’s nothing personal, but I’m wary of claims that are not published.
PS I know who R Moody is.
Mathphys, sorry for blurting out. After the search for, and discovery of, the multi-dimensional Virasoro algebra met with nothing but silence and ridicule for almost 20 years (from physicists, mathematicians have acted very differently), I have become quite hostile per default.
And why should physicists care about genuinely new math, when there are so many exciting new ideas around. Like the anthropic principle and LQG.
Thomas Larsson Said:
“Mathphys, sorry for blurting out. After the search for, and discovery of, the multi-dimensional Virasoro algebra met with nothing but silence and ridicule for almost 20 years (from physicists, mathematicians have acted very differently), I have become quite hostile per default.”
Dear Thomas,
I share you belief on higher dimensional Virasoro and Kac-Moodies although I have a different realization in mind. I share also your frustration. Average colleague does not seem to have the necessary minute or two (or perhaps it is ability after all) to concentrate to a new idea unless it is proposed by authrority.
Lightlike 3-D surfaces X^3 possess X^3-local conformal transformations of imbedding space act as symmetries respecting lightlikeness. Ordinary 1-D Kac Moody algebra emerges naturally as a Kac-Moody algebra associated with the lightlike coordinate and the algebra decomposes into subspaces remaining invariant under the action of this algebra. Infinite number of representations ordinary Kac-Moody are fused to a larger structure. One might think that this could stimulate some interest but landscapeology seems to be more fascinating.
Best Regards,
Matti Pitkanen
MathPhys
I found the commutation relations of the chiral energy-momentum tensor pursuing John Lowenstein’s (the idea came from Wally Greenberg) of “Lie Fields”. in 1973 and presented the results at the January 1974 conference in Rio de Janeiro. In his thesis John did not find any higher dimensional illustration (we now know that there is a no-go theorem) and my finding was the first natural illustration of this concept.
B. Schroer , A trip to Scalingland, Brazilian Symposium on Theoretical
physics, Rio de Janeiro, January 1974, Vol. I, ed. Erasmo Ferreira, Livros T´ecnicos e Cientificos, Editora S. A.
if you give your mailing address I send you a copy.
The Wit-Virasoro algebra, contrary to popular opinion (nobody seems to look at the original Virasoro paper), does not appear in Virasoro’s paper, together with Wit Virasoro does not have the central term and different from Wit he only has the positive frequency (perhaps the reason for missing the central term).
My paper is a structural theorem always including the interacting case. Doing two-dimensional QFT in those days was extremely unpopular (the reason for not sending such things to international journals).
I tell you a funny story which underlines this. At one of the international conferences Swieca was teased by a well-known theoretician (whose name I will not reveal): Andre why do you work on that 2-dimensional stuff? Swieca’s reply: I get lost in higher dimension. Without his sudden death in 1980 the story could have had the following cintinuation: Hy Andre what are you doing these days? S: I am looking at charge screening problems (the Schwinger-Higgs mechanism) in 4-dim. gauge theories. The unnamed physicists: but dont you know Andre that everything happens in two dimensions, in order to understand higher dimensions one only must understand 2-dim. conformal field theory!
MathPhys if you are honestly interested in the rich pre- Wess Zumino-Witten history about 2-dim. models I refer you to a review (published in AOP)
http://xxx.lanl.gov/abs/hep-th/0504206
it is very unfortunate that the connection to the representation theory of current algebras (later loop groups) was cutoff by introducing a Lagrangian terminology which is totally metaphoric and added nothing in substance (in fact the WZW people only pay lip-service to that Lagrangian and continue to compute with the prior current algebras representation theory).
but I genuinely doubt that you are; you seem to be one of those folks who only use weblogs primarily to denigrade others.
Let me remind everyone to please avoid personal attacks here. There is all too much of this going on, it is just annoying and very unenlightening.
Also, Matti and Thomas. Please stop continually trying to use my blog as a forum to promote yourselves and your ideas.
http://xkcd.com/c171.html
MathPhys: You’re moving the goalposts. They don’t call it a theorem, but they don’t always call it a conjecture. And seriously? I’m supposed to show you an example of a serious string theorist? What, are you paying me? I am not an anti-string partisan: I do not have a definitive judgement of the subject. I was sharing with you my personal experience, that I was confused on its status as a conjecture until recently. If that means nothing to you, then what does that say?
There is an established theorem which completely covers the AdS-CFT correspondence, but it has nothing to to with Maldacena (the theorem has been established by Rehren). In fact in my Samizdat essay I have provided additional arguments why the growing suspicion that Maldacena’s conjecture (which links a N–>infinite SUYM with a classical limit of a) 5-dimensional AdS string theory) can be sharpened to an outright contradiction to the theorem.
The confusion comes from interpreting the M-conjecture as an illustration of AdS–CFT correspondence in the sense of the theorem. The M-conjecture maybe correct, the problem is with its interpretation.
What makes the arguments on this weblog so painful is that the sociology of 4000 or so papers wins against a rigorous and clearly presented mathematical theorem. There is no reason to continue this discussion, you can read the paper about the theorem and my arguments in may essay but it is futile to invoke democracy against a theorem.
I encourage people who want to discuss the relation between the Maldacena conjecture and Rehren’s theorem to do so where it is on-topic, at Jacques Distler’s new posting on the subject:
http://golem.ph.utexas.edu/~distler/blog/archives/000987.html
Based on my experience with him, what Distler writes on this kind of subject is often highly misleading (for a recent remarkable example, see what his comments on a recent thread at Clifford Johnson’s blog). I know nothing about Rehren’s argument, so I have no idea what is going on in this case, but encourage people who do know about this to discuss it over there.
Dear Peter,
Thanks, and let me add that this subject is really not appropriate to be discussed in any weblog. Way back in the Sci.PhysicsResearch Archive Rehren tried once, only to be cut down by the ST pittbull. It was that incident which made me aware of the exitence of new barbarians and their attampted sell-out of QFT.
Jacques’ summary looks quite accurate to me.
Dr Scroer, your input is appreciated. Please don’t let some cowardly pitbull discourage your contributions. That person has attacked many of us and GM=tc^3 is still here.
Please, when I referred people to Distler’s weblog, I was encouraging them to read what he has written, and if they want to discuss it, do so over there. I was definitely not trying to start a discussion of this here.