Five years ago the 20th anniversary of the “First Superstring Revolution” was being celebrated, and I wrote some postings about this history (see here, here and here). This month is the quarter-century anniversary, and I haven’t seen any evidence of anyone celebrating.
25 years later, it’s pretty clear that the anomaly cancellation discovered by Green and Schwarz doesn’t actually provide at all the kind of explanation of some aspects of the standard model that people got excited about back then. 1984 also saw the beginning of endlessly repeated and overhyped hand-waving arguments that string theory is needed to cure the perturbative ills of quantum gravity. It turns out that these arguments don’t actually work either. The latest issue of Science has an article about recent discoveries showing that N=8 supergravity amplitudes are much better behaved than expected. Zvi Bern compares the widespread belief that string theory is needed to deal with perturbative divergences to the belief that ulcers are caused by spicy food. While you could make a plausible hand-waving argument for this, it turns out that the real culprit is a bacterium, not enchiladas. According to the article:
The work doesn’t disprove string theory, but it has string theorists backpedaling a bit in their criticism of quantum field theory. “At certain points, our understanding has been incomplete, and we may have said things that weren’t right,” says John Schwarz of the California Institute of Technology in Pasadena. “That being said, the fact is that we still need string theory.”
Forced to concede that a quarter-century’s worth of argument about perturbative amplitudes was wrong, Schwarz tries to shift ground by claiming that the QFT problems are non-perturbative. That may very well be, but until one actually has a viable non-perturbative version of string theory, it will be hard to argue that string theory is the only way to go.
A new review article about quantum gravity describes how things are 25 years after the revolution, with many if not most string theorists having given up hope that string theory has anything to say about unification:
A personal anecdote might best convey the current state of affairs. Early in the spring 2007 semester my University of Florida colleague, Charles Thorn, began a seminar by announcing his belief that:
String theory is just a technique for summing the leading terms in the 1/N expansion of QCD.
After years of hearing more ambitious assessments this was so shocking that I checked to be sure I had understood correctly. Charles confirmed that I had; in his current view, the effort to regard superstrings as a fundamental theory of everything was a blind alley. Later that year I related Charles’ pronouncement to string theory colleagues on three continents and solicited their own opinions. About half of them agreed with him, more often the younger people.
Update: One more, from Martha Stewart, Some Pearls of Wisdom on String Theory.
Richard Woodard’s review article is quite a piece of work—106 pages, and very readable.
PS: From page 62:
In 1997, at Strings in Amsterdam, I happened to sit near Nathan Seiberg. He was extremely angry because Hawking had said that N=8 supergravity was a candidate theory of everything, on par with superstings. Seiberg was really extremely angry, and when I asked to explain, he stopped talking to me.
The day after, Seiberg gave his talk. He was still angry. I have rarely seen a man so angry. He was a missionary, not a speaker. Strings were his religion. I wonder how he deals with all this at present.
Hawking was saying that N=8 Supergravity was the answer in 1980.
It’s just one of the things he does.
There is no point in anyone getting angry about it.
How could N=8 SUGRA be a theory of everything? How could it hold the particles of the SM, any papers on that?
Daniel,
There’s a long literature from the early 80s about this, and the problems with it.
What’s more important is that the N=8 supergravity calculations show that the conventional arguments about the perturbative problems of gravity QFTs are just wrong. The source of these new cancellations is not known, they don’t seem to necessarily require N=8 supergravity.
What’s more important is that the N=8 supergravity calculations show that the conventional arguments about the perturbative problems of gravity QFTs are just wrong. The source of these new cancellations is not known, they don’t seem to necessarily require N=8 supergravity.
I think that goes a bit too far. For example, I don’t think anything is going to make the divergence in pure gravity go away.
Aaron,
I wasn’t saying anything about pure gravity. Again, the point here is just that the standard “only string theory can make QG perturbatively finite” argument appears to have fallen apart. It remains very unclear what is causing these cancellations, and thus for what class of theories they might give perturbative finiteness.
For some relevant speculation, see section 9.3 of 0907.5418 where the authors (for the case of N=4 YM) write: “This perhaps suggests that SUSY is not playing a particularly crucial
role in the story”. They find different helicities coming not from supersymmetry , but from different charts on a Grassmannian.
If I were to indulge in unsupported speculation, it would be that there is some class of QFTs including both gauge theory and gravity for which divergence problems in perturbation theory go away, due to symmetries we do not yet understand. Our world is described by one of these, one that has these still mysterious symmetries (as well as others…).
In 1986, at ICTP, I heard Michael Green say
“Mr Seiberg, look around you. The sky is blue. The birds are singing. Do you really believe you explain all this with E8XE8?”
It was great.
Peter,
You said:
“If, I were to indulge in unsupported speculation, it would be that there is some class of QFTs including both gauge theory and gravity for which divergence problems in perturbation theory go away, due to symmetries we do not yet understand. Our world is described by one of these, one that has these still mysterious symmetries (as well as others…).”
I have it on good authority that Martha Stewart agrees with you. Oh wait… I might be mistaking her with someone else.
“What kind of baking sheet do you suggest using for cookies?”
That should be reformulated!
“What kind of branes do you suggest using for cookies?”
Ok, while we are on the subject of rank sillyness and it’s Saturday, let’s have some popular culture:
http://www.youtube.com/watch?v=63S3vacxI9c
Look out at 7:30 for “Depending on what we find, we _might_ just disprove string theory – that would really make my day!”
Peter: Have you by any chance read this paper by Robert Wald “The Formulation of Quantum Field Theory in Curved Spacetime.” http://arxiv.org/abs/0907.0416 ? In one of your earlier postings to which you have linked in this one, you wrote of U Chicago doing a press release which sang the praises of string theory. A sure sign of change would be what Wald writes in that paper. He describes in detail an algebraic approach to QFT in curved space time which reminds me very much of loop quantum gravity. As if he has thought of a general formalism which describes that employed by LQG and which could work for any other QFT.
Yatima: I love the straight answer she gives to the shredded financial documents question. Like it doesn’t bother her at all.
Certainly the conjectured finitiness of N=8 Sugra is intriguing, and I suspect will be proven sometime soon with the twistor techniques that are hot in development.
Otoh its somewhat strange to disparage string theory using this particular theory, as its well known that it contains extended objects (pbranes and so forth) in its spectrum.
It really begs the question.
I think you would need to find another finite field theory that includes gravity, which explicitly does not include string theory asymptotic states to make the claim robust.
sounds like you are adjusting to string theory not being unique
Haelfix,
I have heard these arguments about N=8 sugra’s relation to string theory. Could you explain a bit more? You’re saying that it is known that there are stable extended field configurations in the theory. This is cool, but so what? The basic entities in the theory are still fields, not quantized strings. So isn’t Peter justified in claiming the latest developments are a blow to string theory?
Big Vlad,
All arguments about N=8 being a ‘finite field theory’ are about perturbation theory *around a flat background*.
Now you need a solution to the classical field equations to start a well-defined perturbation theory, but there are more solutions out there than the trivial one. One class of this are pbrane solutions, which you should think of as very close cousins of instantons in Yang-Mills theory. These are regular saddlepoints of the action and should be included in the full theory somehow.
Is this important from a physical point of view? Probably, but even in the technically much simpler Yang-Mills theory related questions are hard to answer.
Now there is an embedding of N=8 into string theory (apparently). That is, the perturbation theories is claimed to match in a certain limit. Strings also have non-perturbative effects which are to an extent understood, especially for extremal black holes.
If N=8 is finite, a hard-core string theorist might therefore claim that is due to the fact it is string theory anyway and strings provides information about the non-perturbative sector. Really proving this is very hard to do since the limit taken can lead to unwanted effects (in principle). So hard, that to my mind at the moment it is more a question of faith than anything else.
Hontas Farmer,
Yes I’ve looked at the Wald paper. What Wald is doing is quite interesting, but it doesn’t involve quantizing the metric degrees of freedom. I have no idea what Wald thinks of string theory, no reason to believe that he had anything to do with the press release of five years ago (he’s in a different research group, GR, not particle theory, than the string theorists).
You are correct, in the paper he show no work of his own on quantum gravity. The formalism he describes could work as well for Quantum gravity, as it would for any other QFT. If I understood it correctly all one needs to do is provide a algebra of observables for their theory. No metric, or Hilbert space is specified or required. The observables could be the operators and algebra of LQG, or QED.
I wouldn’t call Wald’s formulation a theory of everything, it’s more like a theory of anything.
Was he not the overall department head of physics at U Chicago five years ago? 😕 I assumed that if he was he would have had to sign off on a press release. Shows what little I know.
Hontas Farmer,
What Wald describes assumes the existence of a fixed background metric (unquantized). You can’t use his formalism to quantize the metric.
An assumption that a department chair would have to sign off on press releases I think assigns far more power to that position than it carries in most American research universities…
Aaron,
this is not going too far. there are even claims that classical gravity could eventually be renormalizable perturbatively. essentially the argument goes like this: you have divergencies at all loop levels, but their prefactors have relations that you can describe with a finite number of equations. so you need to introduce an infinite number of counterterms, but with a finite number of parameters giving relations between them. so in a classical sense, this theory is not renormalizable, but it would still be predictive since the number of parameters is finite.
even the perturbative nonrenormalizability of QG is far from being settled (let alone the nonperturbative one). and this relatively recent discovery of bern about N=8 SUGRA cancellations is another strong hint that we don’t understand any of this as well as we should.
Hello Peter, Hontas Farmer
Sorry if I take the discussion too far here…
QFT in curved spacetime has been a reasearch topic at least since the 1970’ties,
you just try to quantize fields in a fixed curved spacetime instead of Minkowski spacetime.
The idea is to generalize QFT a little bit to include classical gravity effects on fields while
neglecting effects of matter on gravity, i.e. on the spacetime metric tensor.
Since there are many approaches to this topic in Minkowski spacetime, you can ask, which ones work best
in this generalized setting, Robert Wald says that algebraic QFT is what you should use.
In algebraic QFT, the basic object you work with are causal nets of von Neumann algebras.
Have a look at “Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics” from him for this approach,
or at Birrell, Davies: “Quantum Fields in Curved Space” for approaches that most people trained in “classical” QFT
will probabliy find more familiar.
All of this has nothing to do with LQG or string theory, it is just an attempt to combine two well known
frameworks (QFT and GR) without changing one of them in any radical way, to see if anything could be learned from it.
The most famous results obtained here are the Unruh-Effect, Hawking-Radiation and the formula for black hole entropy.
What keeps irritating me is that some string theorists seam to treat these as established facts while mostly ignoring
the whole framwork and some key insights of QFT in curved spacetime, e.g. that the particle concept is highly problematic.
If anyone could point out a discussion of this topic (“what do string theorists think of QFT in curved spacetime”) to me I would be very thankful.
“what do string theorists think of QFT in curved spacetime”
I think that a more relevant question would be “what do string theorists think of STRINGS in curved spacetime” and the short answer is “They think about it quite a lot and consider it to be a very important problem”. Quantizing strings in AdS is one of the most outstanding problems, not only because the background metric is curved but also because of the presence of the background RR flux. One particular non-trivial background where strings were successfully quantized, i.e. the string spectrum was found and multiparticle transition amplitudes were computed using the CFT techniques, is the so-called pp-wave background. For a reference see this paper: http://arxiv.org/abs/hep-th/0202109
Off topic: but it seems that cosmic variance has fallen out of favour amongst your physics weblog links?
Thanks James,
That’s very odd and kind of disturbing. It looks like a bunch of links have disappeared (also interactions.org and Lubos) and I have no idea why. Will try and fix later today…
Dear Guest,
thanks for the answer and the link, I will take a look at the paper.
What I mean by “QFT in curved spacetime” is taking GR as it stands, choose
a “physically realistic” spacetime in the sense of classical GR and put quantum fields on it.
“Physically realistic spacetime” in this context usually means a 4 dimensional causal (let’s agree on globally hyperbolic)
classical spacetime. In this sense the moment you think about AdS (5 dimensional or AdS_5 × S_5 as in the paper you referenced), you are not doing “QFT in curved spacetime”.
I do not wish to imply that AdS and quantizing strings in AdS is irrelevant, but can we agree that it is a totally different topic than
“QFT in curved spacetime” as understood here?
I would still be interested in an answer to my original question then…
To Tim vB, if you are interested in this topic, check out these arXiv papers: http://tinyurl.com/mdxobn
Re Links: some have been restored but, for example, Chad Orzel is still left out in the cold.
Incidentally, I’m not just trying to nitpick! As well as visiting your blog because I enjoy reading it, I use it as a jumping off point to other good blogs (except I can’t if the links have vanished!)
Please restore order to my blogverse! 🙂
Peter wrote:” … the anomaly cancellation discovered by Green and Schwarz doesn’t actually provide at all the kind of explanation of some aspects of the standard model … ”
Once I made the mistake to email Distler for some details of the anomaly argument. Though I sent him a friendly mail, I got no answer, but a series of really unfriendly ad hominem remarks. He is clearly a person to avoid contact with, even if you want to talk about string theory.
Hi Guido,
please do not judge people by an episode like this, I am very glad that some string theorists like Jaques Distler
still care to discuss and explain basic topics online.