The Cao-Zhu paper at the Asian Journal of Mathematics that is supposed to have a complete proof of the Poincare and geometrization conjectures is still not available, but the introduction to the paper has been posted there.
If you’re not getting enough string theory bashing today, head over to John Horgan’s Scientific Curmudgeon blog, where he has a posting entitled Pulling the Plug on Strings. It contains a wide selection of string-puns (or whatever you call such things), and he has decided to refer to string theory advocates as “yarn-heads” and braniacs. For his trouble, his comment section is under assault by the usual suspects. There’s also this site, containing a graphic mentioned here before which I refuse to admit to finding funny. The proprietors have an interesting way of dealing with the comment section.
Sabine Hossenfelder has an excellent posting on Science and Democracy.
This past week I’ve spent some time at the 26th International Colloquium on Group Theoretical Methods in Physics, being held here in New York at the CUNY Graduate Center. It was ably organized by Sultan Catto, who somehow convinced me to give a short talk on the blog and the book, one where I think I disappointed people by keeping string-bashing to a minimum. I enjoyed seeing people at the conference, and there were some good talks, including one by Greg Moore on his recent work with Dan Freed and Graeme Segal (see here and here).
Urs Schreiber has been putting his notes on-line about elliptic cohomology. Lots of interesting material, but his comment that he expects the landscape of superstring theories to be equal to the spectrum of elliptic cohomology sounds frightening. Maybe he means a different landscape…
I was quite sorry to hear of the recent death of Irving Kaplansky. Kaplansky was an algebraist, and director of MSRI when I was there in 1988-89. At the time I wasn’t much interested in algebra, so didn’t talk to him about math, but he was responsible for making MSRI a really wonderful place to work.
Update: The slides from Yau’s talk at Strings 2006 are now available here.
I think that Peter was right not to use this jacket in the end: “Superstrings” should be in the plural, and having basic mistakes like this only gives ammunition to critics.
Re Urs:…but his comment that he expects the landscape of superstring theories to be equal to the spectrum of elliptic cohomology sounds frightening.
Maybe he just means that rederiving the landscape rigorously will put a solid nail in the Landscape as a physical idea.
I meant coffin thereof, of course.
The fun of making things precise: you suddenly actually know what you are talking about. š
The space of 1d SQFT is homotopy equivalent to the K-theory spectrum. That’s a theorem.
It is a conjecture (well motivated, though) that, similarly, the space of 2dSCFTs is homotopy equivalent to the spectrum of elliptic cohomology.
(Of course you need to make precise what these QFT spaces are. You do this by looking at certain transport functor spaces.)
Actually, that’s an old idea. Segal has proposed 20 years ago in the last section of his paper on elliptic cohomology, that CFTs should be elliptic cocylces, roughly.
The statement has been refined and sharpened, and brought a little closer to being provable, in the last ten years by Stephan Stolz and Peter Teichner.
I gave the talk in our seminar in front of a mixed audience of mathematicians and string theorists. So I simply went ahead and mapped some math terms to the corresponding string terms.
Under that dictionary, “space of SCFTs” becomes “landscape”.
All up to some details.
Ah, and maybe this is a good opportunity to mention that it was in particular Aaron Bergman who originally made me aware of these topics and of the relevant literature. Thanks a lot!
From the John Horgan article:
That’s a very damning statement, for any scientific theory. Science has always been rolling back the fog of ignorence and mysticism. For any science to reintroduce it is a cardinal sin.
Urs
Please correct me if I’m wrong, but AFAIK SCFT would only describe one sector of the Landscape…and the evidence for the Landscape that some people take to be most compelling does not belong to that sector.
Hi Peter,
thanks for the link to my post.
I am still at reading your book, and I just found that you formulated some of my concerns about the specialisation much clearer than I could ever had (pp 205):
“This huge degree of complexity at the heart of current research […] means that a huge investment in time and effort is required to master the subject well enough to begin such research. […] Since the whole subject is so complicated and difficult, theorists trying to evaluate what is going on often rely to an unusal extend not in their own understanding of the subject, but also on what others say about it.” (possible typos are entirely mine)
Best regards,
B.
Ok, of course I am talking about the space of all SCFTs (but including all information about the possible D-branes for a given SCFT, and also, in particular, all possible worldsheet phenomena like worldsheet instantons). That’s what the conjecture would apply to.
So maybe I should say “perturbative landscape” instead of “landscape”.
“Moreover, even if most physicists no longer take the theory seriously, stringy memes will continue to infect the culture at large. New Age authors in particular have embraced string theory. The appeal is obvious. Along with such quasi-scientific notions as Gaia, complexity theory, psychoanalysis and the anthropic principle, strings entwine the publicās imagination not because they explain the world but because they mystify it.”
As a researcher in granular systems I certainly must take some offense with this notion of complexity being first of all lumped in this group and additionally with the very statement that it is somehow mystifying nature.
I am not here to discuss the merits of chaos however, but rather to state that it is not an argument to suggest that someone’s misappreciation of science reflects upon the subject itself.
I have often encountered individuals with significant misunderstandings pertaining to heisenburgs uncertainty principle, special relativity or a variety of other physics. That in no way diminishes the validity of these as proper scientific theories, and it should not ultimately reflect on string theory, regardless of that theories actual scientific validity.
NM
Nicholas,
About string theory, I think Horgan is right, it isn’t explaining how to unify physics, it is mystifying the issue. About complexity theory I have no opinion. Horgan is trying to be provocative. If you’re provoked, you should take it up with him.
At the risk of an ‘off topic’ comment, I take it Nicholas M. hasn’t read Horgan’s ‘End of Science’.
For NM and others who haven’t read it, my proverbial internet 2 cents is …. read that book!!! Seriously, Horgan’s book is interesting / entertaining for numerous reasons; including aspects of science journalism, philosophy of science, string theory, cosmology, “chaoplexity”, evolution, neuroscience / AI etc (such as narcissitic personality disorder / hubris kicked up copious notches).
Since several of those topics (ST, cosmology, phil of science, sci journos) are repeatedly addressed at ‘Not Even Wrong’, readers here might well appreciate the book (even if they don’t agree with the general thesis).
Horgan’s pretty insightful in general, he doesn’t pull his punches, and at times he’s damn funny!
Back in 2003, I wrote week197 of This Week’s Finds to explain some stuff Stephan Stolz told me about elliptic cohomology. Elliptic cohomology studies a space by mapping it into some spaces called “tmf(n)”, for “topological modular forms”. These spaces are currently understood only in an indirect way. Some people conjecture that tmf(n) is roughly the space of supersymmetric conformal field theories of central charge -n. There’s a lot of evidence that something like this is true.
The space of such theories is not the same as the “landscape” studied by string theorists today… but, it’s still an intimidating structure. If the conjecture is true, this structure has a lot more order to it than one might at first guess!
I can also recommend ‘End of Science’ as a well written series of fleshed-out interviews on the general topic of whether fundamental discoveries in science are behind us (and touching on strings as one example). I enjoyed discussing the subject before and after that book was published, and was dismayed when colleagues would crudely dismiss the arguments Horgan put forth based on his ‘lack of credibility’ rather than putting forth an actual counterargument. John Maddox’ rebuttal book was pretty weak and only led me to think more highly of Horgan.
I’ll have to read it again, but I suspect it’s held up just fine in the last decade.
Urs,
I still find your statment above confusing.
If you include “all information about the possible D-branes for a given SCFT, and also, in particular, all possible worldsheet phenomena like worldsheet instantons”, then you should say “landscape” rather than “perturbative landscape”.
Can you make the statement of the conjecture really precise, please?
Also the way that you type your notes on the web site using html makes them less than fully readable. Why not use Latex and post a pdf file. It’s a pity when so much work is less than fully readable.
MathPhys,
D-branes appear as boundaries of the worldsheet CFT. Worldsheet instantons are essentially worldsheets wrapped an (small) non-trivial two-cycles in spacetime; despite being non-perturbative they are well under control in a worldsheet description. Thus including these effects is possible in a string-loop expansion, which is what Urs meant by “perturbative”. At generic points in moduli space the string-loop expansion is not useful, something people like Peter Woit love to complain about.
Thanks, Michael.
Which browser are you using?
I have tried not to use any symbols that are displayed only after the user installs extra fonts.
I am currently sitting in some random internet cafe, and the formulas in that entry are fully readable and displayed nicely using
– either plain Mozilla Firefox
– or MS Internet Explorer with the free MathPlayer plugin plugin installed (takes 2 seconds)
But you are of course, right, I could have produced a pdf instead.
Not really precise, but more precise than I did before.
I guess it should go like this:
Conjecture: The space of all 2-functors from superconformal 2-paths to graded 2-Hilbert spaces carries a topological structure and is homotopy equivalent to the tmf spectrum.
This is not really precise, yet, for a couple of reasons.
1) Nobody has yet a good idea of how precisely the 2-category of superconformal 2-paths looks like. Its 2-morphisms are superconformal disks with two marked points on their boundary. Horizontal composition seems to be troublesome. But Hilbert Uniformization might help here.
2) When I talk about 2-Hilbert spaces I am indicating that this is the true structure which is secretly behind the vonNeumann algebra bimodule bicategory that Stolz/Teichner use. In fact, I am pretty sure that what they discuss is the special case of a 2-vector bundle associated to a String-2-bundle, using a representation of the string 2-group on 2-Hilbert spaces.
Urs,
I can read your formulas (I’m using IE 6.0), but the layout is awkward (lines are too long, etc) and things are sort of all over the place. I would like to be able to download what you are write in a clean way and read it, annotate it, etc.
A pdf file of a latex document will give you a lot more versatility. You can also build on it in the future, if you want to, and turn what you write into papers.
Re science, I’m trying to understand what you’re saying, and not let your overuse of “decategorification” put me totally off the subject.
Hm, for some reason this happens on some configurations. Not on the ones I am looking at at the moment, though. I guess that in general Firefox is the better option.
I guess you mean categorification instead of decategorification. And its meant precisely to help you to understand what is going on. Whithout it, there is hardly a chance. It is a tool that organizes apperently intricate ideas in a conceptual way.
So that’s why I emphasize, in that entry (in the second but last part) the situation for the toy example of 1-dimensional supersymmetric field theory and K-theory.
If you understand this example, and you know how categorification picks every item of this example and increases its dimension by one, you understand the main idea of the conjecture that I stated.
Actually, the main idea becomes pretty obvious then. All that remains are some technicalities. That’s what categorification does for you: it provides you with all the big picture and the general ideas. All that remains to be done then is figuring out the technicalities.
I’d be happy to try to answer more detailed questions. But maybe we should do that over on the SCT, lest we run into off-topic territory here.
John Baez wrote:
BTW, I do list TWF197 together with other relevant literature available online at the beginning of the first entry of the series.
But that’s mainly because the landscape studied by string theorists today is a small subspace of the full landscape, namely that subspace whose points satisfy a number of phenomenological prejudices and technical restrictions, like being large volume CY compactifications with fluxes.
Maybe I am wrong, but it seems to me that asking the question “Which of 10^500 large volume CY flux compactifications is chosen, and why?” is only a small subquestion of the full question, and motivated mainly by constraining the full question by available and/or expected phenomenological input.
Thanks, Urs, for your kind offer, which I intend to take you on (and too bad for the German soccer team).