Terry Tao’s article What is Good Mathematics?, written for the Bulletin of the AMS, is now available at the arXiv.

There’s a new article also on the arXiv by Zvi Bern et al. explicitly constructing the 3-loop 4-point amplitude of N=8 supergravity. They find various extra cancellations beyond those expected from supersymmetry, and argue that this and other calculations “strongly suggest that N=8 supergravity may be finite.” The innumerable claims made over the years at the beginning of pretty much every string theory book or popular article that you definitely can’t quantize gravity just using QFT are now no longer operational. There is quite a lot of interest in this topic, with an array of possible computations that need to be done in order to sort this out. Just at the Mathematics Institute at Oxford the past few weeks there have been talks related to this by David Dunbar, Kellogg Stelle, Bo Feng, and Michael Green. The Resonaances blog has a report about a talk by Lance Dixon, one of the co-authors of the new paper. Also a nice report on a talk about supersymmetry by David Kaplan, who gives an excellent definition of fine-tuning of parameters: “a model is fine-tuned if a plot of the allowed parameter space makes you wanna puke” (accompanied by an illustrative plot of the situation in mSUGRA).

I’m waiting for the above news about supergravity finiteness to hit the media, perhaps some of the people working on this need to get to work on their press releases. There’s yet more press about the Distler et. al. “test of string theory.” The Daily Texan has an article called Test May Prove Far-out Theory, where Distler explains how the LHC seeing effects consistent with unitarity, analyticity and Lorentz invariance will provide “more evidence” for string theory. The reporter who wrote this called me up, and includes a garbled version of what I had to say. I was trying to be polite and stick to just pointing out that the paper at issue was not a string theory calculation and its title had been changed to remove reference to string theory, something I suggested the reporter might want to ask the paper’s authors about. He seems to have not taken up my suggestion. I probably should have just used more straight-forward language, something along the lines of “dishonest bulls**t”.

The US Congress finally finished dealing with the FY2007 budget, sending a bill to the president which he’ll sign. It restores money to the NSF and DOE, avoiding a freeze at FY2006 levels that looked possible for a while and would have forced shutdowns at Fermilab and RHIC.

Finally, Capitalist Imperialist Pig informs us that Princeton is taking the occasion of shutting down its parapsychology lab to also close down its string theory program and redirect the funds to research on global warming. Somehow I suspect this may be a bit of an exaggeration, but they do seem to be making moves away from string theory and towards phenomenology, sponsoring workshops next month on Physics at LHC: From Experiment to Theory, and Monte Carlo Tools for Beyond the Standard Model Physics.

Update: Here’s a link to the Kaplan talks on SUSY.

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1. Greg Biffle says:

Lance Dixon was a TA of mine when I was an undergrad.

I think he was a postdoc at the time, but he was better than the professor, and we always went to his sessions.

I look forward to reading his paper! Thanks!

2. kuos says:

Question for discussion: how many of these attributes identified by Tao apply to string theory?

• A field which becomes increasingly ornate and baroque, in which individual
results are generalised and refined for their own sake, but the subject as a
whole drifts aimlessly without any definite direction or sense of progress;
• A field which becomes filled with many astounding conjectures, but with no
hope of rigorous progress on any of them;
• A field which now consists primarily of using ad hoc methods to solve a collection
of unrelated problems, which have no unifying theme, connections, or purpose;
• A field which has become overly dry and theoretical, continually recasting and
unifying previous results in increasingly technical formal frameworks, but not
generating any exciting new breakthroughs as a consequence; or
• A field which reveres classical results, and continually presents shorter, simpler,
and more elegant proofs of these results, but which does not generate any truly
original and new results beyond the classical literature.

3. John A says:

At last, Princeton has the guts to shut down PEAR aka “if you stare hard enough at random numbers you’ll see a pattern”

4. Q says:

“… Princeton is taking the occasion of shutting down its parapsychology lab to also close down its string theory program …”

These are unifiable, at least according to the paper of Nobel Laureate Professor Brian Josephson of Cambridge University, http://arxiv.org/abs/physics/0312012 :

“String Theory, Universal Mind, and the Paranormal … A model consistent with string theory is proposed for so-called paranormal phenomena such as extra-sensory perception (ESP). Our mathematical skills are assumed to derive from a special ‘mental vacuum state’, whose origin is explained on the basis of anthropic and biological arguments, taking into account the need for the informational processes associated with such a state to be of a life-supporting character. ESP is then explained in terms of shared ‘thought bubbles’ generated by the participants out of the mental vacuum state. The paper concludes with a critique of arguments sometimes made claiming to ‘rule out’ the possible existence of paranormal phenomena.”

I suspect that those who don’t like string theory have formed a conspiracy to suppress research into paranormal extra dimensions, or ESP mental vacuum states, in case paranormal research come up with some evidence to support M-theory. Hopefully string theorists like Lubos Motl (who is deeply concerned about global warming issues) will take great comfort from the fact that the money being spent by Princeton on string will in future go to global warming.

5. JustAnotherInfidel says:

From what I recall, people tried to do model building with N=8 SUSY a long time ago because it automatically contained a graviton, and so was automatically N=8 SUGRA. There are 28 spin = 1 bosons in the multiplet, which look suspiciously like the adjoing of SO(8). But SO(8) doesn’t contain SU(3) x SU(2) x U(1), and I don’t know any more than this. I guess one could study, say, N=8 SUSY SO(10) or something, and have SUSY break at the planck scale to N=1 SUSY.

I dont know—does anyone know about any phenomenology which has been studied along these lines?

6. kramnik says:

The point with this is not that N=8 might be the TOE that we want. Rather, if it is finite it’s probably due to some as yet unknown deep symmetry which we don’t know about. Determining whether it is finite, and if so why, will be a major clue to uniting gravity with the rest of physics.

7. andy says:

At first I was sure that it was a joke, but the phrase “mental vacuum state” does in fact appear in the abstract referenced by Q.

8. Peter,

My remark about Princeton’s getting out of the string theory business was unmitigated bullshit. I thought I had implied that pretty clearly in the post, and apologize to anyone who was thereby misled.

Mea culpa!

9. Jean-Paul says:

The only reason to be excited about finitness of N=8 sugra is that it’s an existence proof of a finite QFT with spin 2. From the particle physics point of view this is as irrelevant as the vanishing of c.c. in N=1 case.

10. Gordon says:

CapitalImperialistPig:
unmitigated bullshit.

I don’t see why one should be excited if N=8 sugra were finite. That theory certainly has as least as much problems with experiments as string theory. Besides, QFT infinities are not just a nuisance, but something which explain some experiments via anomalies, e.g. pion decay. Could really that effect be reproduced if the SM were embedded in some finite field theory?

12. A String Theorist says:

Hi Peter,

In the abstract, at least, they were very careful to quantify the word “finite” with by saying “perturbatively finite.” I don’t know anyone who even would speculate that N=8 might actually be finite also NON-perturbatively. Presumably the non-perturbative completion of N=8 supergravity would be some string theory.

Take N=4 Yang-Mills theory as an example. It is perturbatively finite, and its non-perturbative completion is a string theory (namely, type IIB string theory on AdS5 x S^5).

13. Ah Godon, coming from you, that means so much!

14. Tim says:

Peter,

you write “on the arXiv by Zvi Bern et. al. explicitly” but “et” means “and” in latin and is not an abriviation thus needs no dot.

Tim et al.

15. woit says:

A String Theorist,

I’ve heard many claims about string theory providing an “ultraviolet completion” of a QFT, but you are the first person I’ve heard claim that it provides a “non-perturbative completion” of QFT. Actually, I think you just got this completely backwards: every string theorist I’ve heard say anything like this has said it in the other direction. No one knows what non-perturbative string theory is, but AdS/CFT can be interpreted as saying that the N=4 SYM QFT (which is believed to make sense non-perturbatively) provides a “non-perturbative completion” of string theory, where we only have a perturbative definition.

Thomas,

I think kramnik has it right. The point is not that N=8 supergravity is a viable TOE, it is that this result says there is some structure in it we don’t understand that is causing unexpected cancellations improving its ultraviolet behavior. The conventional wisdom that QFT’s involving gravity inherently have bad behavior in the ultraviolet looks like it is just wrong. This may be quite analogous to what happened with asymptotic freedom: up until 1973 the conventional wisdom was that QFTs in general had bad ultraviolet behavior, behavior that furthermore was inconsistent with observed high-energy scaling. That change in conventional wisdom killed off string theory once, it could happen again…

Tim,

Thanks, I always forget that. Fixed.

16. Robert Musil says:

According to the NY Times, various “legitimate” scientists visited PEAR’s and even gave them money from time to time. There is a unconfirmed rumor that Ed Witten was hard at work trying to move thought bubbles with his mind when the Princeton Dean rudely turned off the PEAR’s lights, plunging the special ‘mental vacuum state’ into darkness and making Ed stub his toe on the way out.

17. A String Theorist says:

Hi Peter,

Yes I realized right after submitting the post that I was being imprecise.

The essential problem, as you point out, is that we don’t have a non-perturbative definition for “N=8 supergravity”. I would bet that if someone someday finds such a definition, it will end up being a string theory.

18. Hmm says:

It is a stunning indication of americas descent into mediocrity that you are now being contacted by journalists to give views on *scientific* rather than sociology-of-science matters. Wow. Its enough to have a blog; you don’t need to have a record of research accomplishment or to even understand the technical claims being made. God help us all!

19. A String Theorist says:

Oops, I hit submit before I was finished.

About N=4 Yang-Mills, I never said that string theory provides the non-perturbative definition of YM.

I said that the non-perturbative completion of the theory (which you may take to be a Feynman path integral, or lattice I suppose) is a string theory (i.e., in a certain regime of parameter space, it describes relativistic strings).

20. The reporter who wrote this called me up, and includes a garbled version of what I had to say … I probably should have just used more straight-forward language, something along the lines of “dishonest bulls**t”.

Peter, I’m having the same problem these days talking to journalists who want to bullshit up their quantum computing stories (“the world’s first commercial quantum computer has been unveiled, able to solve NP-complete problems in a heartbeat…”). I patiently explain to them why the story doesn’t mean anything like what they think it does, but I get the sinking feeling, even as I’m talking, that the article will have zero mutual information with anything I say. If you ever figure out how to dissuade a journalist from writing the misleading piece he or she wants to write, please let me know.

21. woit says:

A String Theorist,

Thanks for the clarification. I still think it’s kind of misleading to talk about a “non-perturbative” completion of N=4 SYM. By itself N=4 SYM is inherently a non-perturbative theory (even if we don’t completely rigorously understand it). One doesn’t talk about the “non-perturbative completion” of QCD, QCD is just inherently a non-perturbative theory, and going to a supersymmetric version doesn’t change this.

I haven’t thought much about this, but it’s not clear to me that you can’t just define N=8 supergravity non-perturbatively as the path integral, and try and make sense of this. If this works, you would have a purely conventional QFT for quantum gravity. Like many QFTs it might have some regime where a string theory approximation was useful, but I don’t think that would justify calling it a string theory since it is fundamentally defined in terms of quantum fields, not strings.

Hmm,

My, some of you string theory partisans are charming, especially the ones too cowardly to put their names to their ad hominem attacks. I’ll leave it to informed people to decide who was giving this reporter honest, accurate information, me or Jacques Distler.

Scott,

Similarly, if you figure how how to stop journalists from writing the “quantum computers solve NP-complete problems in a heartbeat” story, let me know and maybe it will help me figure out how to dissuade them from the “string theorists figure out how to prove string theory” stories which they are being continually led to write.

My concern about combining anomalies, which are experimentally confirmed consequences of QFT infinities, with a finite theory are not original. I essentially took the argument from Roman Jackiw, hep-th/9911071, which ends with

“one very important lesson we should take from quantum field theory is not to banish all its infinities. Apparently the mathematical language with which we are describing Nature cannot account for all natural phenomena in a clear fashion. Recourse must be made to contradictory formulations involving infinities, which nevertheless lead to accurate descriptions of experimental facts in finite terms. It will be most interesting to see how string theory and its evolutions, which purportedly are completely finite and consistent, will handle this issue, which has been successfully, if paradoxically, resolved in quantum field theory.”

23. anon says:

“I’ll leave it to informed people to decide who was giving this reporter honest, accurate information, me or Jacques Distler.”

Since you complain that the reporter misquoted you, are we to assume, in contrast, that he quoted Distler accurately?

24. Peter Woit says:

anon,

I don’t think people need to or should base their decisions about this on what the reporter has either of us saying, since he for good reason had trouble understanding what is going on. In my case, you can judge from what I’ve written here on this topic as to its scientific accuracy. In Distler’s you can read the press release the university issued for him, or consider the many other press stories quoting him on this topic. My scientific claim is simple, and it seems that a PRL referee agreed: Distler’s paper isn’t about string theory so can’t claim to have a test of it. Distler seems to be quite clear in his claims to the press that he has a test of string theory that can be performed at the LHC.

Up to you to consider which of those two claims is more scientifically accurate.

25. Robert Musil says:

Peter,

“The reporter who wrote this called me up, and includes a garbled version of what I had to say … I probably should have just used more straight-forward language, something along the lines of “dishonest bulls**t”.”

In general, those who deal frequently with the media come to understand that when a reporter calls asking to speak one has two choices: Speak, and be misquoted – or refuse to speak, and be misinterpreted.

I pray you have the widom to choose correctly.

26. Chris W. says:

Scott and Peter,

I’m afraid that the people you need to dissuade are the editors that have final say on what gets published. (Maybe it goes higher than that.) I suspect that in most cases a reporter who is conscientious in this sense would have trouble continuing to report on science-related stories; he or she would be told that they can play ball, take other assignments, or get fired.

Perhaps there is an editor out there who would like to take issue with this. If so, please post a comment, preferably with some helpful explanation. Try not to blame it on the great unwashed public, ie, your alleged readers.

27. Tim says:

Peter,

You write “My, some of you string theory partisans are charming, especially the ones too cowardly to put their names to their ad hominem attacks.” and this is not the first time you bring up such a remark.

Did I miss the sign “If you post here, you are obliged to give your real name!”?

You chose this type of forum yourself and you know very well that posts can remain anonymous, so why complain? If you chose a different forum (refereed journal, arxiv, conference, etc) for letting the world know what you think, all responses would bear the real name of the respondent. However it is by your own free choice that you use a blog which implies by the very nature of this forum that responses can and will remain anonymous.

Your complaining is analogous to a writer who refuses the advice of his publisher to order high quality paper for a new book but later on complains that the books are worn out too quickly.

Tim

28. Ari Heikkinen says:

“close down its string theory program and redirect the funds to research on global warming”

Heh, that’s funny, as I thought the biggest web-advocate of string theory thinks that global warming is utter nonsense (sorry, couldn’t resist:).

29. island says:

Tim, Peter often knows or can find out who the anonymous posters are, yet he generally keeps their secret from the public, (unless he is being severely harassed), while calling them out for being too chicken to claim responsibility for their unsubstantiated bullshit.

Shut up.

30. Peter Woit says:

Tim,

I don’t encourage people to post anonymously here; I think it would be best if people always used their real names. Personally I don’t post comments on other blogs without using my real name, although I can imagine some unusual situations in which I might choose to do so. But my policy certainly is to allow anonymous comments, and I realize there are many legitimate reasons for people to choose not to use their names. If someone wants to engage in anonymous attacks on me, I’m allowing that. I also have every right to refer to people who decide to do this as “cowardly”.

31. Peter Woit says:

island,

Thanks for the supportive comment, but do try and keep the hostility level down…

It is also true that it’s often not too hard for me to figure out who anonymous commenters likely are. For instance, in the case of “Hmm”, his comment was posted from a somewhat unusual and precisely identifiable location, making it not hard to, with a small amount of research, make a pretty good guess as to who he is.

32. Rugs says:

I have a friend that is an editor for a newspaper (I will leave his name, my name and his paper anonymous so we can remain friends) and when we had a mutual friend die in an accident I got to watch how he dealt with reporters. He wrote out every statement and read the statements to reporter’s one word at a time making sure they wrote each word as he had intended. He was very concerned about how the circumstances of our friends’ death were reported. He not only understands how sloppy note taking can lead to bad reporting he also knows that a sensational story can help a reporters career better than a boring one. Though he doesn’t believe it is done intentionally (I feel a little differently) he does feel human nature will push a simple story in the wrong direction. I don’t know if knowing how a newspaper editor deals with reporters is any help but I sure found it enlightening.

33. Peter Woit says:

Chris W.,

I should say that my experience over the last year or so with quite a few reporters is that they try hard to get things right. They’re not experts in the science involved, and, faced with people making contradictory or hard to evaluate claims, they do the best they can. With one exceptional case of behavior that was worse than I would have guessed goes on, I’ve been pleasantly surprised by the competence and degree of professionalism of almost everyone I’ve dealt with.

The problem with the “physicists finally discover how to test string theory” stories mostly doesn’t come from the people reporting these stories, it more often comes from the scientists involved.

34. Michael says:

Peter,

suppose N=8 sugra is finite and exists at the quantum level. In order for your conclusion that it is a theory of quantum gravity besides string theory to hold, you’d still have to show *that*, namely that it cannot be realized as a string theory. Absent such a proof you could make that claim already about N=4 SYM, which is a sugra theory on an AdS space written in funny variables.

Until someone does this for you (clearly you are not capable of it yourself), it is much more plausible to say that N=8 sugra resisted embedding into string theory so far simply because it doesn’t exist beyond perturbation theory.

So even if I swallow all the ifs buts and maybes you interjected, your line of reasoning has more holes than swiss cheese. Your thinking is really very flaky.

35. Eric says:

Michael, the gravitational degrees of freedom in a SUGRA theory are pretty straightforward to isolate (in contrast to the surprising case of AdS/CFT). If N=8 SUGRA were shown to be finite and a sensible quantum theory, no convoluted rewriting of the theory in a dual string picture, or showing that you can get N=8 SUGRA in particular backgrounds ,will change the fact that you have found a non-string theory of quantum gravity.

36. Michael says:

Dear Eric,
How can you say that isolating the degrees of freedom is “pretty straightforward” if you cannot even show that the theory exists? There might just be another “surprise” in stock for you.

The smart money remains on the reverse logic: N=8 sugra cannot be embedded into string theory, because it doesn’t exist beyond PTB.

37. Peter Woit says:

Michael,

You anonymous string theorists are all such polite folks, always a pleasure to try and have a discussion about scientific issues with you.

“N=4 SYM, which is a sugra theory on an AdS space written in funny variables”

That’s just not true. Even if you believe everything conjectured about AdS/CFT, N=4 SYM is supposed to be exactly dual to a full, non-perturbative string theory, not to supergravity on AdS.

It’s kind of hilarious to see string theorists claiming that N=4 SYM should be understood as a string theory, when they don’t know how to define non-perturbative string theory, except as N=4 SYM.

I don’t think the argument “OK, QFT can also give you finite terms in perturbation theory, just like string theory, but it may have problems non-perturbatively, unlike string theory (wait a minute, we don’t know what string theory is non-perturbatively, other than through the QFT…)” is going to fly.

38. Michael says:

“such polite folks”

Stop whining and talk about the issue!

“That’s just not true.”

For large radius, my statement is perfectly accurate; the generalization is obvious. My point was well taken.

You have failed to address the hole in your logic, which I pointed out. Thanks for nothing!

39. Eric says:

Michael,

I’m not even anti-string theory, but you don’t make sense, and your point is definitely not well taken. Since one of the things you do in SUGRA is quantize the metric, you’ve got a perturbative spin-two field staring you in the face, giving you gravitational interactions, just like the relevant closed string mode in string theory: this is very easy to isolate.

For the large radius limit of an AdS space, yes it is supposed to be well-described by a SUGRA, but this is just an approximation, there’s nothing really to “generalize.”

40. Peter Woit says:

Michael,

Despite your rudeness I’m trying to have a serious discussion with you. I have addressed the issues here, you haven’t. The discussion is not about a limiting case of large radius. All you seem to be able to do here is talk about “the smart money”. If you know of an argument showing that N=8 supergravity can’t be defined outside of perturbation theory, but string theory can, let’s hear it.

41. Michael says:

Peter,
I may have an opinion, but I do not know if N=8 sugra exists. I simply pointed out that under the assumptions you made your logic still had a gaping hole, and it remains so.

You are trying to sidestep the issue and claim string theory isn’t better. Perhaps. Bananas. Whatever. It does not reduce the number of holes in your argument.

42. Ari – Yes, that was whatever point there was of my little “joke.” Lubos had just deleted a global warming comment of mine when I wrote the post.

43. Michael said: “suppose N=8 sugra is finite and exists at the quantum level. In order for your conclusion that it is a theory of quantum gravity besides string theory to hold, you’d still have to show *that*, namely that it cannot be realized as a string theory. ”

If this is the “hole” you keep talking about, you are pegging your argument on a pretty flimsy support. Whether some QFT can be realized (I think you really mean represented) as a string theory is irrelevant to the question of whether there is a QFT of gravity. Perhaps the second law of thermodynamics can be realized as a game of parchesi – if so, it would certainly be amusing, but it would hardly show that parchesi is essential to the description of the world.

44. gunpowder&noodles says:

Michael’s comments are so funny — especially “My point was well taken” [Haha, I thought *other* people are supposed to say that!] that I suspect he is pulling Peter’s leg. Unlike, sadly, “Hmm”, whose determination not to have a sense of humor is known far and wide.

45. Q: Regarding thought bubbles– Thanks for sharing.

46. ObsessiveMathsFreak says:

And for examples of What is Bad Mathematics, see Jean-Pierre Serre’s How to Write Mathematics Badly.

47. mathjunkie says:

What is the importance of that N=8 supergravity exists? Does it mean that it can replace String theory?

48. Alex Nichols says:

There are now two papers:
1) http://www.arxiv.org/pdf/hep-th/0702112
-based on point particles

2) http://arxiv.org/abs/hep-th/0610299
-based on strings

Both claim to be u-v finite.

Question: At what sort of energy levels would it be possible to exclude either 1 or 2?

49. Arun says:

If I understand correctly, crucial to the Bern et. al. argument is the use of the KLT (Kawai, Lewellen, Tye) tree-level relations, orginal expressing tree-level closed-string scattering amplitudes in terms of pairs of open string ones, which in the low energy limit of compactifaction to four dimensions relate N=8 supergravity and N=4 super YM tree amplitudes.

Unless this step could be discovered independently, it would appear that a digression into string theory is essential to the (possible) discovery of viable QFT gravity theories.

🙂