After last month’s posting at Cosmic Variance about how String Theory is Losing the Public Debate, Sean Carroll seems to have decided to go on the offensive (or defensive…), with a piece in New Scientist entitled String theory: it’s not dead yet, which he reproduces and has a posting about here.
I can’t really disagree with Sean about either title. Yes, string theory is losing the public debate, and no, it’s not dead yet. Some of Sean’s claims in the New Scientist piece are descriptive claims about the behavior of theoretical physicists:
String theorists are still being hired by universities in substantial numbers; new graduate students are still flocking to string theory to do their Ph.D. work…
Ideas about higher-dimensional branes have re-invigorated model-building in more conventional particle physics… Cosmologists thinking about the early universe increasingly turn to ideas from string theory.
All of these are true enough (although the word “re-invigorated” might not be the most appropriate one), but don’t address the value judgment of whether any of this activity is a good thing or not. One could also come up with other evidence for continuing activity in string theory, such as the large number of press releases being issued claiming to have found new ways to “test string theory”, but the fact that these have all been bogus is relevant to evaluating whether this activity is a good thing or not.
Sean’s positive case for string theory is mostly about its role as a quantum gravity theory, acknowledging that the Landscape is a problem, and that progress has slowed since the mid-90s (although more accurate would be “come to a dead halt, now moving backwards..”). He describes that period as “it seemed as if there was a revolution every month”, displaying the predilection for over-the-top hype that has characterized much string theory salesmanship over the years. His claims about the achievements of string theory vary from relatively modest exaggerations (“The theory has provided numerous deep insights into pure mathematics”) to standard misleading propaganda:
“a promising new approach has connected string theory to the dynamics of the quark-gluon plasma observed at particle accelerators” (connected? wonder how strong the connection is…)
“it is compatible with everything we know about particle physics” (and also compatible with just about everything we know to not be true about particle physics…)
“Michael Green and John Schwarz demonstrated that string theory was a consistent framework” (there’s a lot more to consistency than canceling that anomaly…)
“It was realized that those five versions of the theory were different manifestations of a single underlying structure, M-theory” (would be nice if we knew what M-theory actually was…)
In the comment section Sean explains how string theorists have no intention of standing behind what used to be considered the main “prediction” of the theory, TeV-scale supersymmetry:
If the LHC discovers supersymmetry, string theorists will be happy, but if it doesn’t there’s no reason to give up on string theory — the superpartners might just be too heavy.
So, prospects for string theory remain bright, since with each new experiment the situation is: heads they win, tails doesn’t count.
Also at Cosmic Variance is the latest in an exchange between Joe Polchinski and Lee Smolin, entitled Science or Sociology? (some earlier parts of the exchange are here). I’m mostly resisting the impulse to get involved in various parts of that argument since Smolin doesn’t need my help: the points at issue don’t seem to me central to the claims of his book, and his positions and what he wrote in the book are perfectly defensible.
While I don’t see the point of arguing about things like how conjectural the AdS/CFT duality conjecture is (pretty damn conjectural I’d think though, since no one even knows what the definition of one side of the duality is…), it is interesting to see what it is that Polchinski finds most objectionable about Smolin’s criticisms. In the context of an argument about how much of a problem the positive CC was considered to be by string theorists in the late 90s, he strong objects to Smolin’s description of “a group of experts doing what they can to save a cherished theory in the face of data that seem to contradict it”, going on to describe the work on moduli stabilization that led to the landscape as “a major success” which Smolin is trying to paint as a “crisis”. Ignoring the argument about who thought what back then (although if you really care about this, for some relevant evidence, see the Witten quote), in a larger sense “a group of experts doing what they can to save a cherished theory in the face of data that seem to contradict it” describes precisely the behavior of Polchinski, Susskind, Arkani-Hamed, and many others in the face of the disastrous situation created by the “major success” of moduli stabilization.
The “anthropic landscape” philosophy is nothing more than an attempt to evade failure, and it is an failure of scientific ethics of a dramatic kind. Once one understands a speculative idea dear to one’s heart well enough to see that one can’t make any conventional scientific predictions using it, ethics demands that one admit failure. Instead we’ve seen scientists announcing a new way of doing science, even writing popular books and magazine articles promoting this. Most physicists (including even a sizable fraction of string theorists) are appalled by this behavior. If you don’t believe me, consult a random sampling of the faculty in your nearest physics department, or watch Susskind’s recent talk in Israel where he describes himself as at the center of a circular firing squad.
Polchinski ends by claiming that Smolin’s case for “group-think” and for a “sociological” problem with string theory is “quite weak”. This problem is obviously hard to quantify and a matter of perspective. While I don’t doubt that Polchinski sees himself as not suffering from “group-think”, if he were, he obviously wouldn’t think so. One thing I think is undeniable about the “sociology” of all this is that the blog phenomenon has put a lot of evidence out there for any unbiased observer to judge for themselves, and this is one of the main reasons for what even a fervent string theory proponent like Sean Carroll has noticed: string theorists are losing this debate.
Anyone who regularly follows the most well-known blogs run by string theorists pretty soon becomes convinced that they have a real problem. Lubos Motl is the Id of string theory on uncensored display. The fact that his colleagues promoted him and show signs of only having a problem with his politics, not his behavior as a scientist (if they have any problem with his calls for my death or other attacks on me, I’ve never seen evidence of it) is truly remarkable. Two out of three recent string theory textbooks prominently carry his endorsement. All another prominent string theorist blogger, Clifford Johnson, has to say about Lubos is “I thank him for his physics contributions and for widening the discussion.” This was in the context of an eight-part personal attack on Lee Smolin and me for having written books that Clifford steadfastly refuses to read. The other of the three prominent string theory bloggers is renowned for his sneering attacks on the competence of anyone who dares to criticize string theory, issues press releases claiming tests for string theory that other physicists describe as “hilarious”, while misusing his position of responsibility at the arXiv to stop links to criticism of string theory articles from appearing there. Among those string theorists without their own blogs who choose to participate in the comment sections of others, a surprising number seem to think that it is an ethical thing to do to post often personal attacks on string theory critics from behind the cover of anonymity. Less anonymously, a large group of string theorists at the KITP seem to have thought it was an intelligent idea to act like a bunch of jeering baboons, on video, for distribution on the web.
This kind of public behavior and the lack of any condemnation of it by other string theorists is what has convinced many physicists and others that, yes, string theory does have a “sociological” problem. I have to confess that my experience over the last couple years has caused me to come to the conclusion that the string theory community has a much greater problem with personal and professional ethics than I thought when I wrote my book. The fact that so many string theorists have decided to respond to my book and Smolin’s not with scientific arguments, but with unprofessional behavior I think speaks volumes for the strength of their scientific case, and this has been noticed by their colleagues, science journalists, and the general public. While I applaud Polchinski for behaving professionally in his response to the two books, I suggest that he should take a look at the behavior of many of his colleagues and ask himself again whether or not there might be a sociological problem here.
It’s possible that the LHC will find something interesting, and this will lead to the next 10 years of hiring in particle theory in physics departments being predominantly non-string theorists (unless the string theorists turn out to be the ones who explain what the LHC finds). This would greatly reduce the political power of string theory. However, I think this is only likely to happen if substantial new and different physics is required to explain the LHC results.
However, I think this is only likely to happen if substantial new and different physics is required to explain the LHC results.
Have you looked at hiring patterns over the past few years?
What? Students are still flocking to string theory? Bummer for them.
Don’t get me wrong, every grad student I know involved in it is having a blast. The thing is, every grad student I know trying to get a job afterwards is just freaking miserable. Saying that string theorists are still being hired by universities in substantial numbers (assuming we actually believe it) hides the fact that many of those universities are little better than high schools and many of the jobs are temporary – and don’t even ask about the pay.
One soon-to-be-phd actually approached me the other day and told me flat out not to finish my degree in physics. I suppose the lesson here is: be careful studying string theory; it may be more than some public debate you lose.
Bad advice. Finish your physics degree and then do something other than String Theory afterwards.
Peter Shor wrote:
unless the string theorists turn out to be the ones who explain what the LHC finds
Homework exercise: find a scenario that string theory *cannot* explain.
As far as I understand it, isn’t it the main problem? Is it not the question that string theory is able to accommodate a huge plethora of solutions? So the only condition I see that would make string theory falsifiable would be in a situation were a physical phenomenon was found such that it *could not* be accommodated in string theory by any means.
Christine
Aaron (and others),
I’d be interested to hear about it if anyone has any actual numbers about this they can point to, other than personal impressions that the job market for string theorists sucks (the job market for all theorists has sucked since 1970, one needs some numbers to see if there have been real changes in relative suckiness…).
My own impression from seeing who is getting hired is that, while leading string theorists are going around giving talks about how one should ignore the fact that current versions of string theory can’t predict anything, because we don’t know what string theory really is, if you actually work on the fundamentals of string theory, trying to make progress on figuring out what string theory “is”, your job prospects are dim. On the other hand, if you work on “connecting string theory with real physics”, doing things like “string phenomenology”, then you have a better chance of getting a job, even though most people acknowledge that this kind of research is not likely to go anywhere.
Homework exercise: find a scenario that string theory *cannot* explain.
As always, I fall back on my amazement that, given the inability of anyone to produce a single vacuum consistent with the real world, people immediately postulate that everything is permissible. But whatever.
For Peter: You can read the rumor mill just as well as I can. In fact, contrary to my expectations (and that of others I know), this year was surprisingly good for formal string theorists. By that, I mean four were hired to physics departments. In addition, there were three more positions (offered or hired) in math departments. Add to that 2 more, maybe, and you get the string theory jobs in this country and Canada. A rough count (I’m lazy) gives me at least twice times as many phenomenology/astro jobs as that.
Aaron,
I did take a look at the latest rumor mill (hey, what’s up with Frederik going to Harvard?) and I just lost all sympathy for string theorist’s complaints about the job situation. By my count there are 32 research jobs offered, very roughly half to people who haven’t worked on string theory at all, half to people whose research has some connection to string theory (often black holes), even if tangential. This is consistent with your count of formal string theorists.
This number of jobs is dramatically higher than it was a few years ago, both for string theorists and non-string theorists. I remember looking at these numbers carefully several years ago, and estimating 15-20 jobs/year, consistent with one I just picked at random (2000) and counted, giving 19 jobs.
So, looks like all the hullabaloo generated by my book and Lee Smolin’s has caused a huge increase in hiring of both string theorist and non-string theorists (or maybe all the people hired 1960-70 are finally starting to retire or croak…).
Anyway, if you believe the Mill, it looks like the job situation for particle theorists, string and non-string, is better than it has been at any time for nearly forty years.
Aaron,
I don’t understand. Is 9 positions really a good number? My university alone will produce 3 graduates by the end of the year. Peter was looking for numbers, so do you have an idea of how many string theory students are graduating and how that compares to the 9 positions that opened up in a good year?
Peter,
I am curious as to your source for your information. I’d love to compare other physics disciplines as well. To be honest, the job market still sounds pretty awful to me, regardless of how it compares to past years.
locrian,
Yes, 9 positions is a good number. These are tenure-track positions at universities that support research, and such positions have always been very scarce in this field compared to the number of people getting Ph.Ds in it.
I looked very carefully at these numbers when I was doing research for my book about 5 years ago. The best estimate I could find was that there were about 80 students a year in the US getting particle theory Ph.Ds, with roughly ten of them ending up in a permanent position. This was based on the fact that the rumor mill was showing roughly 15 hirings into tenure track jobs/year, and an estimate that a third or so of those would not turn into permanent hirings (people would not get tenure or would move some place else).
So, the job situation in particle theory has been awful, and this has been true since 1970. It does appear though that the job situation may be moving from awful (10-15% of Ph.Ds getting permanent research jobs) to less awful (20-25% of Ph.Ds getting permanent research jobs). But, in any case, if you go into this field and get a Ph.D., you’re still pretty sure to not be able to get a job working in it (and pretty much certain to not get one unless you’re working on one of the hot topics in string theory or phenomenology).
Where’d you get half and half? It looked around 2:1 to me.
9 is a good number compared to previous years. Objectively, most people who graduate in string theory won’t get jobs.
Peter: yes, but that is not a reason to pass up the opportunity of doing a physics Ph.D. if one has the opportunity. There are employers outside academic research, and they, generally, are impressed by a Ph.D. in a hard science (although whether (e.g.) the anthropic landscape could be classified as such is debatable).
As for the increased hirings of String Theorists since the publication of “Not Even Wrong”, I would attribute it to the aura of glamour that you have endowed the subject with by lambasting it publicly.
aaron,
I’d characterize things as more like 1/3 string theory, 1/3 hard-core phenomenology, 1/3 less easy to characterize (often cosmology, black holes), but of this last 1/3 a significant number have at least one paper claiming to be related to string theory.
But, I don’t think we disagree about the bottom line, the job situation for string theorists is better than ever (although that for phenomenolgists maybe even more so).
I’d say that this year was a surprisingly good year, especially for formalists. Who knows what next year will be like?
As always, I fall back on my amazement that, given the inability of anyone to produce a single vacuum consistent with the real world, people immediately postulate that everything is permissible. But whatever.
Aaron,
Then tell the prominent theorists who have been acting like a Landscape containing vacua consistent with the real world (however few) is a foregone conclusion to put up or shut up. I’m getting pretty tired of your insistence that people like Leonard Susskind are unrepresentative of most string theorists, while the community of which he is evidently a part allows his viewpoint to gain so much traction. (One should recognize the efforts of David Gross to counteract this phenomenon.)
Let’s restate the problem. Either:
(1) string theory leads inexorably to a landscape of solutions, none of which are consistent with observation or the success of the Standard Model, requiring the abandonment of string theory as a failed project (which is inherently nothing to be ashamed of);
(2) string theory leads to a landscape of solutions, some of which are consistent with observation and the success of the Standard Model, but offers nothing but shallow, after-the-fact empirical criteria for selection (“curve-fitting”) of these solutions, leading to invocations of the Anthropic Principle;
(3) string theory leads to a landscape of solutions, and also incorporates clear criteria for ruling out all but a small family (an equivalence class?) of these solutions on a priori grounds, which thereby become testable, along with the underlying assumptions of string theory itself.
One possible source of the criteria for (3) would be a non-perturbative formulation, or at least some empirically fruitful insights into the required features of such a formulation.
For the record, (2) is logically possible, but is an abdication scientifically—a 21st century version of Ptolemaic astronomy. Physics could have resorted to such a resolution of its problems at any point in its history. On what basis should it become acceptable now? Skeptics of the significance of fundamental scientific discoveries have always invoked variations on the argument that alleged agreement of theories with observation is a fraud and a fabrication, an inscrutable accident of some practical use but telling us nothing about reality, or a kind of tautology, following inevitably from the structure of our minds and senses or the structure of our theories. The risk of vulnerability to these arguments is always present, as is the risk of outright refutation by observation for theories with genuine empirical import. If we choose to run the latter risk we can have no final guarantee of success.
[Thanks, Christine.]
I don’t understand Peter’s claims that comparable numbers of offers go to string theorists and phenomenologists. Let’s look at the current rumor mill data. If we neglect job offers from math departments, there are only 6 string theorists with offers out of 32 total theorists with offers. If we count the ones from math departments, it’s 10 out of 36: close to 1/3, but still substantially less. And the remainder is really dominated by phenomenology, not just 1/3: there are 22 offers to phenomenologists. Below I list the people with offers, categorized appropriately (all due apologies for filing people in boxes, but I want to counter the misperception that’s being spread in this thread):
String theory (10 offers, 4 from math departments)
————–
Frederik Denef
Bogdan Florea (math dept)
Yang-Hui He (math dept)
Matthew Headrick
Chris Herzog
Liam McAllister
Michael Schulz
James Sparks (math dept)
Diana Vaman
Johannes Walcher (math dept)
Phenomenology (22 offers)
————–
Kev Abazajian
Kaustubh Agashe
Rouzbeh Allahverdi
Mu-Chun Chen
Antonio Delgado
Patrick Fox
Ayres Freitas
Michael Graesser
Yuval Grossman
Dan Hooper
Jamal Jalilian-Marian
Ryuichiro Kitano
Ian Low
Markus Luty
Alexander Penin
Tilman Plehn
Stefano Profumo
Yuri Shirman
Peter Skands
Philip Stevens
Tim Tait
Liantao Wang
Other (theoretical cosmology, mostly — 4 offers)
—————
Alfredo Lopez-Ortega
Alberto Nicolis
Dejan Stojkovic
Andrew Tolley
anon,
You might consider actually reading what I write. I didn’t write: “comparable numbers of offers go to string theorists and phenomenologists”, I wrote
“1/3 string theory, 1/3 hard-core phenomenology, 1/3 less easy to characterize (often cosmology, black holes)”
Among your 26 “non-string theorists” are many whose work is not so easy to characterize, but is not what I would call “hard-core phenomenology”. One example is Nicolis, who has been hired here at Columbia, whose recent work is in the “Swampland” program.
Notice I put Nicolis in the “other” category. I’m pretty sure that all 22 of the people I listed as phenomenologists are, in fact, phenomenologists, whether or not you think they are “hard-core.” One could always further subdivide them as collider phenomenologists, astroparticle phenomenologists, model-builders, etc….
Also, while Nicolis is not readily classifiable as either a string theorist or a phenomenologist, he is nonetheless a first-rate theorist and a good example of how the theory community doesn’t exclude people with good, non-mainstream ideas.
Chris W. —
String theorists fight about this stuff all the time, often quite vociferously.
anon.
My definition of “hard-core phenomenologist” was more or less someone who interacts with experimentalists and computes numbers they care about.
I don’t know Nicolis at all, but characterizing as non-mainstream someone who has been part of the Harvard theory group, one of Arkani-Hamed’s main collaborators, and working on the “swampland” program that has been heavily promoted by leading string theorists seems to me rather bizarre.
The only reason I chose him as an example was that I started going down the list at the Rumor Mill and he was the first clear case of what I meant by a non hard-core phenomenologist who has done work related to string theory. So, he was an example purely because “C” for “Columbia” comes early in the alphabet. One could waste a lot of time going through the rest of the alphabet…
Chris,
I agree with your scenario 1-3. How do we decide which of these are most reasonable and when?
Let’s say the MSSM is true. Well LHC results are not yet online, and the MSSM is just as unpredictive as string scenario 2.
It might look like scenario 1 to Peter now, NEW, but maybe after another 50 years of intense sustained research, with LHC results and bootstrapping from that, 2 or 3 actually holds.
Of course it’s possible string theory it’s actually 1, and it is starving off alternative research directions which is what Lee says is the Trouble with Physics.
My own opinion: if LHC doesn’t find SUSY-partners, or its results cannot be accounted for or embedded in, a string theory scenario, I hope the HEP community pursues alternative research directions.
2 alternative post-SM post-string HEP research directions I’d like to see investigated is Smolin’s preon braiding, and condensed-matter analogues such as Volvovik’s fermionic points.
Dan
Sometimes a “negative” result can be just as interesting, such as if the LHC doesn’t find anything at all. (ie. No Higgs particle and nothing else).
“Coin,
While string theory has contributed to mathematics in various ways, as I wrote, I do think that saying it has provided numerous deep mathematical insights is an exaggeration.”
Let me quote from Faddeev/Atiyah’s description of Witten’s work, in the Proceedings of the ICM
(you can see the text here: http://www.icm2002.org.cn/general/prize/medal/1990/Witten/page1.htm ):
“…Although he is definitely a physicist (as his list of publications clearly shows) his command of mathematics is rivalled by few mathematicians, and his ability to interpret physical ideas in mathematical form is quite unique. Time and again he has surprised the mathematical community by a brilliant application of physical insight leading to new and deep mathematical theorems.”
The citation goes on to detail Witten’s insights into Morse Theory, the Index Theorem, Rigidity Theorems, and Knot theory. Essentially, by 1990 Witten had re-invented all of that century’s work in geometry, using his string-theory heuristics.
By the way, this was back in 1990, so it doesn’t count his later work on Sieberg-Witten, or the recent stuff on Geometric Langlands; forget his and other people’s (Candelas, etc) work on Mirror Symmetry, which has completely blown open Moduli of Curves, and deeply influenced the work of Kontsevich and Okuonkov, to name just two Fields Medalists who’ve benefited from string theory…
Just to give one personal example: in 1990, I don’t think anyone expected that there would be a connection between Weyl’s asymptotic formula and Mumford’s conjectures on the Moduli of Curves; the glue of this particular connection turns out to be Witten’s conjecture, and the various proofs by Kontsevich, Pandharipande/Okounkov, and Mirzakhani. That one conjecture has also inspired great work in combinatorics, in representation theory, etc.
As you say, you yourself have written about some of this. Can you explain to me what your criterion for “numerous deep mathematical insights” is, as this certainly qualifies in my book…
Dipankar,
Your Atiyah/Faddeev quote does not mention string theory, precisely because the work that Witten got the Fields medal for has nothing to do with string theory. To say “Essentially, by 1990 Witten had re-invented all of that century’s work in geometry, using his string-theory heuristics.” is non-sense, I don’t believe that’s what Atiyah or Faddeev actually wrote. In particular, the work on morse theory, supersymmetry and the index theorem predates Witten’s interest in string theory and has absolutely nothing to do with it.
If you’re interested in where Witten’s work came from, you might want to try reading my book, which has a chapter on the subject.
Aaron,
That’s good to hear…
“Essentially, by 1990 Witten had…” was from me, not Atiyah. I almost didn’t put it there, since I could guess what the response would be. And indeed, I made a mistake: I should have said “Essentially by 1995…,” and perhaps I should have ended with the canonical locution “using his path-integral oracle”.
Had I done that, then I could have made the following list of results:
– Morse theory
– Atiyah-Singer Index theorem
– Donaldson Theory
– (you get the point)
These are (I think you’ll agree) several of the handful of crowning accomplishments of 20th century geometry. And I’ll note that this is why Witten, at the AMS Alg Geo conference at Santa Cruz in 1995, made the (very compelling to everyone I knew who was there) argument that, in the future, QFT would be a field of mathematics alongside of algebra and analysis, and would probably subsume differential geometry, algebraic topology, and even parts of alg geo).
Certainly, this does _not_ mean that he re-invented algebraic topology, hodge theory, etc, in terms of the basic definitions. But he definitely re-cast our understanding of such things, in much the same way that Grothendieck re-cast our understanding of algebraic geometry. Atiyah and Bott have both written about how Witten completely re-organized the way that _they_ think about Morse theory, about their own work on Yang-Mills, etc. Similarly, Witten’s results on Atiyah-Singer and Donaldson theory weren’t just new proofs, they were fundamentally new ways of thinking about these problems, very much “deep insights”. A flurry of work and consolidation and connections followed, in each case (as I’m sure your colleague John Morgan would agree).
You distinguish between this work of Witten’s and “Witten’s interest in string theory”. I find this disingenuous, though perhaps it is exactly this point that distinguishes our world-views.
Green Schwarz and Witten is copyrighted 1987. That tells me that Witten was pretty busy thinking about String theory precisely when he made his great original math discoveries. And certainly the Seiberg-Witten work and the Geometric Langlands work is from his “string theory” era, if we are to try and force “periods” onto his career?
But I think this is a key point: I believe that String theorists are by and large engaged in a basic, long-overdue, formal, fundamental study of QFTs. QFTs are where the problem started, since they showed (1) the incredible power of perturbative methods, (2) the lack of mathematical rigor in the methods, and (3) underscored the depth of the problem Einstein had wasted the last ~30 years of his life pursuing (Feynman-Schwinger-Tomonaga showed us how successful QFT was, and thus how crazy it was to think that the problem of unification was a tractable problem in 1920).
The Jaffe-Quinn school was one approach, but it got bogged down. String theory has become the de facto place where a basic study of QFTs is taking place (and why not, since if you’re a budding grad student hoping to learn QFT, you probably want to turn to your phenomenologists and your string theorists, since they’re the experts on QFT in your department, no?).
The actual sociological problem might be this: Einstein was lucky; Gauss and Riemann had already discovered the necessary math for him, so he didn’t have to invent it for GR. Unfortunately “mathematicians” like you and me are blogging when we should be proving hard math theorems; as an indirect result, physicists studying QFTs are having to invent the mathematics for themselves. One can easily imagine that Einstein and a handful of grad students would have taken >20 years to invent Riemannian Geometry; well, it’s taking us >50 years to invent the necessary math for QFT. So it goes.
Because of this world-view of mine (shared by many, I think), separating the results that Witten obtained by studying QFTs from his work in string theory – well, this is very weird to me, since it was surely his interests in string theory that had him write his papers on TQFTs, etc.
Dipankar,
I really suggest that you learn some of the history of this subject, you might find it enlightening. Just one example: Witten’s work on Morse theory and supersymmetry (which is the foundation of his work on TQFT) dates from 1980, his interest in string theory began around 1983, with his first paper on the subject in 1984.
The “path-integral” is not “string theory”. These are two very different things. QFT is not string theory either. You’re welcome to your view that I am “disingenuous” or “weird” for pointing out that many of Witten’s most important ideas come from another source than string theory, but this happens to be a fact. The interaction between different ideas about physics and mathematics is a complicated and extremely interesting subject, I’d suggest you try learning something more about it than that everything is due to “string theory”.
Your reply seems to prove my point: you distinguish between supersymmetry and string theory here, while I believe elsewhere the lack of experimental evidence for supersymmetry is an oft-repeated example of one of the failures of string theory (perhaps not by you? my problem here is undoubtedly that I’ve arrived late to a debate where all the principal players are already nursing wounds from attacks from all sides).
Certainly, when Zumino said (in the 70s) that supersymmetry implied SU(n) holonomy, that wasn’t string theory either. And yet SU(n) holonomy and the exchange of supersymmetries are exactly the key features of Mirror Symmetry.
In ’81, Witten was writing about Kaluza-Klein theories, and the “Supersymmetry and Morse Theory” paper wasn’t published until 1982 (of course I don’t doubt you that it was written earlier – this is before my time). In general, most of these geometry results come from duality of one kind or another.
Your point is that I should read more and learn to distinguish between supersymmetry and string theory, whereas my point is quite clearly that I think these are false distinctions that ignore the fundamental point: in reality we’re paying people to study QFTs.
Couldn’t I use your same arguments to say that string theorists themselves are in a different field today than they were 20 years ago? The string theorests of today are basically studying a completely different subject (geometric langlands? category theory?) from the string theory of 20 years ago.
The commonality between string theory then and now? Some mix of supersymmetry, kaluza-klein, and the basic (distinguishing) notion that the fundamental objects of the universe are strings.
You seem to be saying that only the last element is string theory. I’m saying that all of it is QFT (my version of “can’t we all just get along?”)
I commented on this thread, because it seemed to me that you were saying that this interaction between math and physics hasn’t provided deep insights for mathematics, which sounded like bad advice for a beginning grad student. Now I see you’re drawing a particular distinction (one which I don’t agree with, and not because I’m so ignorant of the literature/history, as you suggest; rather my interpretation is fundamentally different).
If I were a beginning grad student in math, I might easily conclude from your comments that reading Witten’s papers wasn’t fruitful. That sounded really bad to me; in fact, Kontsevich’s ’94 ICM talk tells me that, if you’re interested in math, you might do very well indeed to think hard about physics in general, and string theory in particular.
With that, I should withdraw.
…woops, memory failing me, I think Zumino only showed U(n) holonomy…
Dipankar,
“you distinguish between supersymmetry and string theory here”
“If I were a beginning grad student in math, I might easily conclude from your comments that reading Witten’s papers wasn’t fruitful.”
This is just completely ridiculous. Supersymmetry and string theory are two different things, and I’ve written voluminously about both of them and about the importance of Witten’s work, on this blog and in multiple chapters of my book. In all of these places I’ve made it very clear that I have the highest opinion of Witten’s work, that the experience of reading some of his papers has been among the greatest intellectual experiences of my life. But, you know, he’s written more than 300 papers, despite what you think they’re not all about string theory, and, surprisingly enough, some are more interesting than others.
I came to your website because a friend pointed me to your informative post about the abc conjecture. Because I liked to that post, I went to the previous post, and then read about how you thought Sean Carroll was mildly exaggerating string theory’s influence on math, followed by comments that were fairly condescending towards Polchinski, both of whom I have a lot of respect for. This surprised me – especially the comment about string theory’s influence. So I read the comments, to see if anyone else questioned this statement. Someone did, and your comment reinforced the point that string theory was no big deal to mathematicians.
So I didn’t read your voluminous writings about how great Witten is. I reasonably conclude that others might first encounter your website the way I did, and draw the conclusions about your opinions that I did. Hence my post.
My mistake to post in the first place – I didn’t know what I was up against. You clearly have long ago formulated very strong opinions on all of this, and seem to be very ready to jump down my throat when I question the validity or (more importantly) _usefulness_ of the distinctions that you’ve drawn.
You’ve clearly rejected my umbrella metaphor, that physicists are drawing false distinctions between what they do, when all they’re trying to do is understand QFT. I don’t see any point to string theory, or supersymmetry, or Kaluza-Klein theories outside of understanding QFT, and so hence it’s all QFT to me.
Fine, you reject this. But you still don’t address my other points: that Witten was _thinking_ about string theory, and hence using string theory heuristics to guide his work on moduli of curves, on seiberg-witten, on geometric langlands. that in itself is interesting and deep.
Second, that mathematicians studying QFT in general and (yes) string theory in particular (or at least conjectures that grew out of string theory) resulted in deep work not only in mirror symmetry, but in fundamental algebraic geometry (Mumford’s conjecture, which was proven by Madsen and Weiss largely because of the renewed interest around moduli of curves sparked by Kontsevich’s proof of the Witten conjecture), in combinatorics (Ravi Vakil’s article in the Notices gives a nice presentation of that work), and in representation theory.
There are more examples, obviously (Givental’s work is of course important, and there are a number of conjectures in that area that have fallen recently, and I think we’ll find that Okounkov’s work will soon combine with Werner/Schramm’s work to show the power of stochastic methods in general; certainly Okounkov is influenced by string theory). Renewed interest in old topics, new problems solved – all of this is at least in part due to mirror symmetry. I wouldn’t be surprised if the geometric langlands thing led to similar revolutions throughout math.
anyways…
Very harsh language in addressing me. Did I do/say something to deserve condescension like “Despite what you think they’re not all about string theory”? I apologize about the mistake I made about a Zumino paper from the 70s, but perhaps you could cut me a little slack on a comment on a blog, and consider that I’m not a complete idiot? I don’t think it requires stupidity and/or ignorance to disagree with you on the precise borders between gauge theory, supersymmetry, QFT, TQFT, and string theory. While clearly these are separate topics, they are interconnected in everyone’s head. It’s like saying that the fundamental theorem of algebra is only a theorem in analysis, cause there’s no algebra involved in the proof (unless you do the Galois theory proof, or somesuch…) – technically true but misses the point a little, I’d say.
Actually, forget what I’d say. Your views are also not representative of either the physics or the math communities, and your admonishment/directive for me to read your book are not convincing me that these communities have a reason to change their behaviours, nor does your condescending tone elicit in me an overwhelming compulsion to buy your book.
Dipankar,
You’re the one who came here, started posting highly misleading comments that showed you don’t know what you’re talking about (no, path integrals, supersymmetry and string theory are not all the same thing), and started insulting me as being “disingenuous” and “weird”. Given that behavior, I’ve actually tried to respond as politely as I can manage, giving you some factual information you might consider before going on in the way you do about Witten, TQFT and string theory. If you read more than a couple postings on this blog, you might find, in addition to a point of view that challenges your prejudices, some accurate information of interest.
Re. the discussion of jobs to string/brane theorists vs others, one curious aspect revealed by the rumor mill page is that the string/braners are generally being hired sooner after their PhD, and with fewer papers. Now why might that be?…
I guess their brilliance must just be so abundantly clear that there is no need for them to prove themselves over longer periods, in contrast to the non-string plodders.
Care to cite evidence that string theorists are being hired younger than non string theorists?
It was a pain, but here’s some data: it’s the people listed as having recieved job offers at research uni’s on the current U.S. rumor mill page as of this moment. I’ve ordered it according to the year they got their PhD’s, and in the format “Person – N – topic(s)” where N is their current number of publications according to Spires. The people in each PhD year are listed in order of increasing N. Simple data analysis follows below.
—————————
2006:
McAllister 12 string cosmo
2004:
Tolley 13 stringy cosmo
Profumo 38 astro, susy pheno
Skands 39 susy pheno
2003:
Headrick 16 string
Hooper 78 astro
2002:
Nicolis 16 cosmo (recently stringy)
Sparks 17 string
Fox 17 branes, some susy pheno
Florea 20 string
Delgado 25 brane models
Chen 34 pheno (beyond SM)
Herzog 35 string
Kitano 37 susy pheno
He: 55 string
Freitas 61 susy pheno
2001:
Low 27 pheno (branes & trad)
Stojkovic 29 cosmo (non-string)
Walcher 30 string
Vaman 33 string
Abazajian 37 astro
2000:
Allahverdi 42 cosmo (susy & stringy)
1999:
Denef 27 string
Graesser 31 susy pheno, some branes and astro
Penin 55 pheno (trad)
Tait 56 pheno (trad & branes)
1998:
Agashe 44 pheno (beyond SM, branes)
Plehn 70 susy pheno (brane-free)
1997:
Shirman 29 susy pheno, branes
Jalilian-Marian 58 pheno (trad)
1996 & earlier:
Luty 68 susy pheno, cosmo, a bit of branes
Grossman 90 pheno (mostly trad)
Excluded from data:
Wang (since he already got a job last year)
———————
Average PhD year for string theorists (including stringy cosmology): 2002
Average PhD year of those for whom strings and /or branes is a major component of their research: 2001
Average PhD year of those for whom strings/branse is not a major research component: 2000
That’s a less pronounced difference than I had expected, but it’s still definitely there. Also, there is a clearly discernable tendency for string/brane theorists to have fewer paper than other job recipients in the same PhD year, although there is admittedly a fair bit of fluctuation in that.
amused: your counting is also a little skewed because several of the phenomenologists are moving from one faculty job to another (Grossman, Luty, …)
Care to cite evidence that string theorists are being hired younger than non string theorists?
And if it is true, does it mean “string theorists are more likely to be hired” or “string theorists are more likely to be young”?
“I guess their brilliance must just be so abundantly clear”
Maybe somebody can explain this to me, because I just don’t understand. How is it even possible to be brilliant in a subject like string theory as there are no experiments (and likely never will be) to validate or invalidate your work…The “Not even wrong” logic would to me imply, also, “Not even brilliant”, since physical correctness of ones work is a requirement of ones work also being brilliant. Or have I missed something here?
Therefore, I conclude any hiring of string theorists cannot be based on brilliance, at least not in string theory, no matter how much they might wish to think otherwise…
I have a dumb question:
Why can’t String Theory be thought of as a 2-d QFT(CFT)? I mean, what makes ST to be different from just a particular 2-d CFT?
ok,
A CFT is defined on a fixed Riemann surface with conformal structure. To get perturbative string theory, you need to integrate over all Riemann surfaces (i.e., sum over the genus, and integrate over the moduli space for each genus. This introduces a new parameter, the string coupling.
And this (divergent) series is supposed to be an asympotic series for the true string theory, whatever that is. You’re supposed to be including branes, M-theory, etc….
anon.: Ok, I wasn’t aware of that, but I suspect it also applies to string theorist Denef. It surprises me that the rumor page doesn’t list these people under `faculty shuffle’.
LDM: In fairness to string theorists I think there is a reasonable formal theory sense in which ST work can be “brilliant” despite the lack of connection to experiment. The ads/cft correspondence and dualities between various theories are examples (at least in my book). Whether brilliant string work is overhyped and oversold compared to brilliant work on non-string topics is a completely different question…
Amused,
The whole point is to get a number. When I was in grad school, I knew a very bright Chinese student who had devised a formulation of QFT in terms of measure theory, which he thought was significant because he viewed the concept of a measure space somehow more “fundamental”. But unfortunately, he could not get any new predictions with his new theory.
Similarly, who cares about Maldacena’s Ads/Cft, if it does not ultimately get related to an experimental number?
An example of a duality which I would currently consider superior to Ads/Cft, from the point of view of physics, would be the Legendre transformation. This is an example of a duality which actually does produce measurable numbers, in both classical mechanics and thermodynamics.
Usually, a 2-dimensional CFT is defined on all Riemann surfaces. (Except, possibly, in some older statistical mechanics literature.)
In a quite precise way, a CFT is a functional that reads in “Riemann surfaces with marked points” and spits out numbers (the “correlators”).
The basic idea of perturbative string theory is that one defines a theory on some “target space” by looking at a sum of values of a fixed 2-dimensional CFT evaluated over all Riemann surfaces.
The choice of the fixed CFT here is the choice of “target space background”.
This idea is supposed to be the direct generalization of how perturbative quantum field theory works: there we sum the correlators of 1-dimensional QFT (known as “relativistioc quantum mechanics”) over all 1-dimensional graphs of sorts.
Instead of pairing 1-dimensional QFTs with graphs, as perturbative quantum field theory on target space does, perturbative string theory pairs 2-dimensional QFTs with surfaces (to be thought of as “smeared graphs”).
Urs,
Of course, you are right: it is the modern terminology to define
a CFT as something on any given Riemann surface. But it is not
an especially physical viewpoint, at least not for some situations. Should we define any quantum field theory on all manifolds of a given dimension? Why stop there, and not consider all dimensions? Just as with CFT, one could regard any QFT as a functional giving correlators from the manifold.
I think the utility of such a definition depends on the problem
being studied.
Thanks everyone for the clarification.
LDM,
Studying the structures of QFT’s (of point particles, strings,…) with the aim of getting deeper insights into them, finding relationships between them etc is a valid activity in its own right, even if it doesn’t lead directly to numbers that can be compared to experiment. It is intrinsically interesting (in the same way that pure math is interesting), and the ideas generated and lessons learnt may later turn out to be very important for “real physics”. (Yang-Mills theory was an example.) Actually there is quite a bit this kind of activity going on in particle theory these days, ST is far from the only case. For example there is the “fuzzy physics” approach to QFT’s, and a few years back there was quite a bit of “quantum groups” activity with luminaries like Faddeev being involved. I don’t think any of that was likely to directly lead to new numbers to compare to experiments. The point was to generate new theoretical insights. The complaint that ST doesn’t produce new (or any!) numbers applies just as well to those other activities. The reason no one complained about them though was that they never became so dominant in formal particle theory to the extent that people who chose not to work on them were putting themselves at a disadvantage careerwise.
Yes, indeed, we should!
That’s one way to make precise what an n-dimensional quantum field theory is: it is a functor
nCob –> Hilb
namely a rule which reads in n-dimensional manifolds with boundary, assigns Hilbert spaces to the boundary components (the “spaces of states”) and assigns linear maps between these to the manifolds themselves: this is the quantum propagator
U(t)=exp(it H)
in simple cases, or, more generally, the path integral for the given states on the boundaries.
If this sounds obscure and “remote from physics”, notice that this is, read the other way around, nothing but a clean formalization of what the “path integral” defining the QFT should really be.
Ever wondered how physicist manage to start their papers by writing down an ill-defined expression called the path integral and then nevertheless extracting lots of interesting results at the end of their paper?
There is a simple reason behind this: while the definition of the path integral as an integral mostly makes no sense at all, it often happens that this definition is in fact never used at all! Instead, what is being used are a list of properties that the path integral supposedly satisfies.
The most important of these is “sewing”: this says that evaluating the path integral for a process from A to C is the same as doing it from A to B and from B to C and “summing over all intermediate states”.
It is common practice in math to isolate those properties of the objects under considerations which are actually used in the constructions, theorems and proofs.
Here, it is essentially the sewing law (and also the unitary condition). The technical term for something satisfying such a law is a “functor”.
So, we notice that whatever the path integral actually is, it is at least required to be a functor that reads in cobordisms and spits out morphisms of Hilbert spaces (or numbers, “correlators” if the manifolds fed in have no boundary.)
Once we are at this point, we do the obvious and declare that every such functor qualifies as a “path integral”, hence as defining a quantum field theory.
So an n-dimensional quantum field theory is — by definition — a functor from n-dimensional cobordisms to Hilbert spaces.
For a discussion of this geared towards physicists, check out some notes by Kevin Walker.
And indeed, one does!
The slogan is this:
Quantum field theory is the study of representations of cobordism categories.
But it’s tough working out in detail what these functors are like, obviously. Most of the progress has been made, of course, for the simplest cases: topological field theory in 0,1,2,3 dimensions and conformal field theory in 0,1,2 dimensions.
With the advent of Khovanov homology, people are now with more intensity attacking 4-dimensional topological QFTs in this precise sense, see the recent Conference on Link Homology and Categorification in Kyoto and especially Gukov’s talk Gauge Theory and Categorification
Certainly. Especially, if the problem is “understanding what’s going on” and “organizing one’s concepts” this is very useful.
‘So an n-dimensional quantum field theory is — by definition — a functor from n-dimensional cobordisms to Hilbert spaces.”
This is a starting point for TQFT, not for QFT in general.