Endless Universe

Posted on June 2, 2007 by woit

There’s a new popular book about cosmology now out on bookstore shelves, Endless Universe by Paul Steinhardt and Neil Turok. The authors are the inventors of a competing model to inflationary cosmology, variously called “ekpyrotic” or “cyclic” cosmology. They describe coming up with the same idea simultaneously during a lecture at Cambridge on M-theory by Burt Ovrut back in 1999. Ovrut was describing his work on the Horava-Witten scenario, which involves two parallel branes (we live on one of them), and during the lecture both Steinhardt and Turok started wondering about whether one could explain the big bang as a collision of branes. They went up to discuss this with him after the talk, and continued the discussion on a train ride to London that evening to see a performance of the play Copenhagen. This train ride was a central part of a 2002 BBC TV program Parallel Universes and a recent play Strings by Carole Bugge that I saw performed here in New York late last year.

The book is very much an advertisement for cyclic cosmology, and devotes a lot of space to doing something which is rarely done, explaining the problems with inflationary cosmology. Steinhardt has worked extensively on coming up with viable inflationary models, and a large part of the book explains the story of this research. Perhaps the most interesting aspect of the book is the story that Steinhardt and Turok each tell about their careers and how they ended up working together on this alternative to inflation. The problems with inflation are described in the context of promoting their cyclic model of branes colliding, moving apart and then back together in a repeating pattern. They heavily sell the idea that a cyclic model with no beginning of time is conceptually much preferable to a standard inflationary model in which the universe emerges at a given time. Reading this made clear to me why, at the recent String Cosmology meeting here in New York, Turok was so persistently questioning one speaker about whether everything he was doing didn’t just depend on an unmotivated choice of initial conditions.

Steinhardt and Turok do a pretty good job of demolishing the inflationary multiverse and the associated Anthropic Landscape philosophy that has become so popular in recent years. They correctly describe the main problem with the inflationary multiverse as the lack of any way to test the idea, even in principle, making it not really a scientific idea at all. As for the testability of their own theory, they devote an entire chapter to the question of contrasting its predictions for the CMB with those of inflation. They claim that both cyclic and inflationary cosmology make the same predictions for the WMAP results (implicitly criticizing the commonly made argument that WMAP provided strong support for inflation). The one possible test that they point to that could distinguish the inflation and cyclic scenarios is the expected more sensitive measurement in coming years of a possible B-mode polarization signal due to gravity waves in the CMB. They claim that inflation predicts a significant amount of B-mode polarization, whereas the cyclic model doesn’t. Unfortunately, from what I can tell by looking at the recent literature on “string cosmology” (e.g. here), various inflationary scenarios can give a wide range of amounts of such polarization, with stringy models like “brane inflation” and “modular inflation” leading to essentially none, just like in the cyclic case. So, I guess the cyclic model is in principle falsifiable, if next generation CMB experiments turn up measurable B-mode polarization. But if this doesn’t happen, I don’t see how one is ever, even in principle, going to distinguish experimentally between the cyclic and inflationary scenarios, which will make this whole area of research highly problematic.

On the whole the book seems to me to be too much of an advertisement for a very speculative idea, and I don’t think the public needs more of this in this kind of format. I didn’t notice anything in the book about what the case against cyclic cosmology might be, so anyone who wants to find out the other side would have to go on a search of the scientific literature, something most members of the public might not be able to do. Most strikingly, since the cyclic model is based on brane ideas motivated by string theory, the book contains endless hype about string theory, without so much as a word about its problems. One would have to read extremely carefully to realize that there is not a shred of experimental evidence for string theory. As for recent public debates about the problems of string theory, the authors just pretend they don’t exist. They give a long list of recent popular books in this area, such as those of Susskind and Vilenkin promoting the Landscape, but somehow neglect to include the two such books that have taken a critical point of view on string theory.

Associated with publication of the book, it looks like there will be various stories in the media promoting the cyclic vs. inflationary debate, trying to make it into a modern version of the old steady-state vs. Big Bang controversy. On the Edge web-site there’s a recent piece by Turok, which gives a good explanation of his current research and point of view. From NPR, there’s a very recent radio show about the cyclic model, entitled Forget the Big Bang Theory, where “renegade physicist” Turok’s model is described as “fighting words in the halls of science.”

Posted in Book Reviews | 29 Comments

Even More Stuff Than Usual

Posted on May 31, 2007 by woit

Here are various things of interest that accumulated while I was away:

Last week there was a conference in Florence on the early history of string theory, some of the talks are available here.

Lots of blogging activity among Fields Medalists: there’s a lot worth reading in Terry Tao’s reporting on a series of lectures by Yau at UCLA here, here and here. At the blog of fellow Fields Medalist Alain Connes, there’s mention of on a recent conference at Vanderbilt (slides here), as well as a report from Connes about a recent conference on the philosphical ideas of Wolfgang Pauli. Finally, yet another Fields Medalist, Richard Borcherds, has a blog. Not only do Fields Medalists like to have blogs it seems, but they also like to use them to discuss physics…

Some other blogs I’ve run across include A Strange Universe, from gravitational wave physicist Warren Anderson, which includes his Dire Straits inspired Papers For Nothing. Also John Armstrong’s The Unapologetic Mathematician, which has a lot of expository material, and Julie Rehmeyer’s MathTrek, a blog at the Science News web-site.

Steven Weinberg has canceled a planned public talk at an event to be held in conjunction with PASCOS 2007 at Imperial College in London in July, an event celebrating the 50th anniversary of the arrival of Abdus Salam at Imperial. In a letter to Mike Duff (available here), Weinberg says that he is boycotting the event in response to news of a boycott of Israel by the British National Union of Journalists, due to his belief that there is no possible explanation of this other than widespread anti-Semitism in Britain “especially in the intellectual establishment” or “a desire to pander to the growing Muslim minority in Britain.” Note: any attempts to use mention of this news to justify attempts to carry on the Israeli-Palestinian conflict in the comment section of my blog will be ruthlessly suppressed.

As usual, Tommaso Dorigo is doing a great job of making current collider physics actually seem exciting and interesting. He’s now spreading rumors of a 4-5 sigma excess of multi-b-jet events being seen by D0. What does CDF data show? He’s keeping his mouth shut about that… Maybe there will be some excitement at the upcoming summer conferences…

There’s a new Harvard College magazine about math, run by undergraduates called The Harvard College Mathematics Review. The first issue contains an article by Noam Elkies about the abc conjecture, and one by Dennis Gaitsgory about how not to teach linear algebra.

Via Mathephysique, here’s an interview with theorist Edouard Brezin.

I keep running across more and more web-sites of theory groups that are putting up material from their theory seminar talks. The latest is the HEFTI Seminar Archive at Davis.

Mike Hopkins gave a Distinguished Lecture Series in Toronto recently. Only audio from the talks is available on-line, and I can attest that forcing someone to try and follow a talk they are interested in like Mike’s The Topological WZW Space of Conformal Blocks just by listening to the audio without always being able to tell what he is writing on the board is just cruel.

Via the n-Category Cafe, notes from a recent conference in Kyoto on Link (also known as Khovanov) homology and categorification. Lots of interesting talks to read, but I’m especially fond of the abstract of Dror Bar-Natan’s talk, which begins:

I’m over forty, I’m a full professor, and it’s time that I come out of the closet. I don’t understand quantum groups and I never did.

Now I don’t feel so bad. Also, for inspiration, check out his Dream Map.

Update: A Chicago network news show has a recent segment about Fermilab and the hunt for the Higgs.

Update: The D0 rumor has made it to Slate.

Posted in Uncategorized | 33 Comments

Proof of the abc Conjecture?

Posted on May 26, 2007 by woit

While I was traveling this past week, there was a conference held here entitled L-functions and Automorphic Forms, which was a celebration of the 60th birthday of my math department colleague Dorian Goldfeld. From all I’ve heard the conference was a great success, well attended, with lots of interesting talks. But by far the biggest excitement was due to one talk in particular, that of Lucien Szpiro on “Finiteness Theorems for Dynamical Systems”. Szpiro, a French mathematician who often used to be a visitor at Columbia, but is now permanently at the CUNY Graduate Center, claimed in his talk to have a proof of the abc conjecture (although I gather that, due to Szpiro’s low-key presentation, not everyone in the audience realized this…).

The abc conjecture is one of the most famous open problems in number theory. There are various slightly different versions, here’s one:

For each $\epsilon >0$ there exists a constant $C_\epsilon$ such that, given any three positive co-prime integers a,b,c satisfying a+b=c, one has

$$ c < C_ \epsilon R(abc)^{1+\epsilon}$$ where $R(abc)$ is the product of all the primes that occur in a,b,c, each counted only once.

The abc conjecture has a huge number of implications, including Fermat’s Last Theorem, as well as many important open questions in number theory. Before the proof by Wiles, probably quite a few people thought that when and if Fermat was proved it would be proved by first proving abc. For a very detailed web-site with information about the conjecture (which leads off with a quotation from Dorian “The abc conjecture is the most important unsolved problem in diophantine analysis”), see here. There are lots of expository articles about the subject at various levels, for two by Dorian, see here (elementary) and here (advanced).

As far as I know, Szpiro does not yet have a manuscript with the details of the proof yet ready for distribution. Since I wasn’t at the talk I can only relay some fragmentary reports from people who were there. Szpiro has been teaching a course last semester which dealt a bit with the techniques he has been working with, here’s the syllabus which includes:

We will then introduced the canonical height associated to a dynamical system on the Riemann Sphere. We will study such dynamical systems from an algebraic point of view. In particular we will look at the dynamics associated to the multiplication by 2 in an elliptic curve . We will relate these notions and the questions they raised to the abc conjecture and the Lehmer conjecture.

For more about these techniques, one could consult some of Szpiro’s recent papers, available on his web-site.

The idea of his proof seems to be to use a and b to construct an elliptic curve E, then show that if abc is wrong you get an E with too many torsion points over quadratic extensions of the rational numbers. The way he gets a bound on the torsion is by studying the “algebraic dynamics” given by the iterated map on the sphere coming from multiplication by 2 on the elliptic curve. I’m not clear about this, but it also seems that what Szpiro was proving was not quite the same thing as abc (his exponent was larger than 1+ε, something which doesn’t change many of the important implications).

Maybe someone else who was there can explain the details of the proof. I suspect that quite a few experts are now looking carefully at Szpiro’s arguments, and whether or not he actually has a convincing proof will become clear soon.

Update: I’m hearing from some fairly authoritative sources that there appears to be a problem with Szpiro’s proof.

Posted in abc Conjecture | 19 Comments

The Empire Strikes Back

Posted on May 25, 2007 by woit

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.

Posted in Uncategorized | 129 Comments

This Week’s Hype

Posted on May 24, 2007 by woit

Still traveling, but will be back soon. This week’s bogus “test of string theory” is described in a NASA press release about three satellite-based experiments that would look for violations of the equivalence principle. From the press release:

…it [a violation of the equivalence principle] could provide the first real evidence for string theory. String theory elegantly explains fundamental particles as different vibrations of infinitesimal strings, and in doing so solves many lingering problems of modern physics… The equivalence principle could offer one way to test string theory…

“Some variants of string theory predict the existence of a very weak force that would make gravity slightly different depending on an object’s composition,” says [Clifford] Will. “Finding a variation in gravity for different materials wouldn’t immediately prove that string theory is correct, but it would give the theory a dose of supporting evidence.”

…string theory makes a range of predictions about how strong this new force would be, so it’s possible that the effect would be too small for even these space-borne instruments to detect.

Does string theory predict violations of the equivalence principle? From a posting on Lubos Motl’s blog:

In reality, it will probably be impossible to falsify string theory because string theory is probably correct and you can’t ever falsify correct theories. 😉 But if string theory were wrong, there would be thousands of ways to falsify it, even in the very near future. Although string theory predicts many new phenomena whose details are not uniquely known, it also implies that many old principles are exactly valid. If string theory is correct, the superposition principle of quantum mechanics, Lorentz invariance, unitarity, crossing symmetry, equivalence principle etc. are valid to much higher accuracy than the accuracy with which they have been tested as of 2006.

If you believe that string theory is wrong, just prove any of the theories predicting all the bizarre phenomena like Lorentz symmetry breaking, breaking of unitarity, locality, rotational invariance, and so on. I think that all these things are badly motivated – but it’s mostly because I know that it seems that they can’t be embedded in string theory. If you don’t believe string theory, you should believe that anything can occur and every new test of Lorentz invariance has a potential to falsify special relativity. Every new test has a potential to falsify the equivalence principle. And there are dozens of such examples. Without string theory, all these laws are approximate accidental laws and symmetries. I assure you that string theory will pass every new test of this type and its foes will always lose. String theory allows us to redefine what proposals about new physics are reasonable and what proposals are not, even without the exact knowledge of the vacuum.

I guess it’s all right that I don’t have time to comment on this, since no comment seems necessary…

Posted in Uncategorized | 33 Comments

All LHC, all the Time

Posted on May 15, 2007 by woit

The LHC media blitz is in full swing, with last week’s long New Yorker article now followed by an unusually long and detailed New York Times piece titled A Giant Takes On Physics’ Biggest Questions. Dennis Overbye does an excellent job of covering the story. Besides the experimentalists actually involved in building the machines, he quotes theorists John Ellis, Joe Lykken, Nima Arkani-Hamed and Michelangelo Mangano. To distinguish this piece from the New Yorker one, here it’s Mangano who is the one who consumes a lot of espresso. There are side-bars about the recent problem with the Fermilab magnets and about the implications for string theory (not much). There’s a multimedia component to the Times coverage, with interactive graphics, a slide show, a podcast (an interview with Arkani-Hamed, described as “one of the physicists at the center of the project”), and a video.

I do fear all this LHC coverage is peaking too early. With still probably at least a year to go before the machine even starts taking data, the coverage may already be generating an LHC overexposure problem: see Chad Orzel’s new posting Tired of the LHC. If Chad is already complaining about this, boy is he going to be grumpy about it by a year from now…

The New Yorker keeps its physics theme going this week with cover art that includes a blackboard full of basic equations from quantum mechanics.

The NY Times article includes the usual not very cogent explanation of the role of the Higgs. For something much better aimed at explaining Higgs-hunting to the general public, see the online interactive presentation Hunt for Higgs, part of a web-site about the LHC called Big Bang.

Blogging may be light the next week or so since I’ll be traveling. First stop is Trieste, where I’ll be speaking at 5pm on Friday as part of a large event there called FEST. From there I’ll make brief visits to Geneva, Paris and London, back here in New York late next week.

Posted in Uncategorized | 71 Comments

New Blogs and Other Stuff

Posted on May 12, 2007 by woit

Here’s a few new blogs I’ve run across recently:

  • The FQXi organization now has a blog called FQXi Community.
  • Rantings of an Angry Physicist is not another Not Even Wrong, but an interesting blog so far devoted to explaining what is going on in Steve Carlip’s quantum gravity course.
  • The new open access journal PhysMathCentral has a blog. It’s “open access” in the sense that it promises to indefinitely provide free access to published articles. Funding comes from the authors of the articles, who have to come up with an “article processing charge” of around $1500. I’ll be curious to see if this funding model works out, but have my doubts. From what I remember, back in the 1970s, the fact that APS journals were charging authors a similar “Page Charge” fee was one of the reasons why many prominent theorists stopped publishing in the Physical Review and started publishing in commercial journals like Nuclear Physics B, thus entrenching commercial publishers like Elsevier. It’s unclear to me now how many authors will be willing to pay to publish when they can publish for free in other (often commercial) journals.

Robert Bryant, a great geometer in the Cartan-Chern tradition, now at Duke, has accepted the post of next director of MSRI at Berkeley. Robert was here at Columbia recently as a visiting professor, and I think he’s a wonderful choice for leading MSRI.

The Geometry, Topology and Physics Seminar at UCSB has some material from talks there on-line. Last month there was a quite interesting talk by Sergei Gukov on gauge theory and “arithmetic topology”, meaning some analogies between 3-manifold topology and number theory.

For the past few days in Brussels there has been a Solvay workshop on “Gauge Theories, Strings and Geometry” . Talks are available here.

From the Fermilab Steering Group trying to develop a strategic roadmap, there’s a presentation about possibilities for higher energy colliders than the LHC or ILC. Ideas discussed include a doubling of the LHC energy using new 17 Tesla magnets, and a huge proton-proton collider called the VLHC to be built deep underground, in the Chicago area.

Next month in Paris there will be a Smolin/Damour debate about string theory, see Dispute chez les physiciens.

For an interesting article I just ran across about Geoffrey Chew and S-matrix theory during the 1960s, see here.

Posted in Uncategorized | 19 Comments

Crash Course

Posted on May 7, 2007 by woit

This week’s New Yorker has a quite good article on the LHC and the state of particle physics with the title Crash Course. One of the main themes of the article is that of the rivalry between experimentalists and theorists. There’s a quote from Leon Lederman:

If I occasionally neglect to cite a theorist, it’s not because I’ve forgotten,… It’s probably because I hate him.

CMS experimentalist Robert Cousins describes worries that triggers designed with too much attention paid to theorists could be disastrous:

There are famous high-energy-physics experiments that missed discoveries because they weren’t writing them to tape… This is why we try not to be too specific about which theoretical speculations we care about. We add up all the energy, and if it’s a huge number we write that event to tape. If on one side of the detector it’s a not-so-huge number, but there is nothing on the other side, so it’s a huge imbalance, we get excited about that, and we write that to tape, too.

The only theorist interviewed is Nima Arkani-Hamed, who, while consuming prodigious numbers of espressos, describes the perception of theorists by experimentalists as:

There is a sense among many experimentalists that theorists are a bunch of irresponsible little spoiled brats who get to sit around all day, having all these fun ideas, drinking espresso and goofing off, with next to no accountability.

and jokes that theorists will need to get a “Deep Throat” among experimentalists in order to get access to any raw LHC data.

As for the state of the LHC, the Resonaances blog at CERN describes rumors from “well-informed sources” that the low-energy test run scheduled for late this year is likely to be cancelled, with a physics run at full energy not likely until summer 2008.

Posted in Uncategorized | 21 Comments

Witten on 2+1 Dimensional Gravity

Posted on May 6, 2007 by woit

The high point of Friday’s string cosmology workshop here in New York was Witten’s lecture on his new ideas about 2+1 dimensional quantum gravity. I’ll try and reproduce here what I understood from the lecture, but this (2+1 d quantum gravity) is not a subject I’ve ever followed closely, so my understanding of the topic is very limited. It does seem clear to me though that Witten has come up with a striking new idea about this subject, linking together some very beautiful mathematics and physics. He has yet to write a paper on the subject, but presumably there will be one appearing relatively soon. I also suspect this is what he’ll be talking about at Strings 2007.

Witten began by stating his motivation: to study fully quantum black holes in an exactly solvable toy model. There’s no exactly solvable model in 3+1d, and 1+1d is too simple, so that leaves 2+1d. Assuming 2+1d, for positive cosmological constant Λ he is suspicious that the theory is non-perturbatively unstable and one can’t get precise observables, for Λ=0 one doesn’t have black holes, so that leaves negative Λ, here the vacuum solution is anti-deSitter space, AdS3.

Quantum gravity in AdS3 is related to 2d conformal field theory. There have been studies of AdS3/CFT2 as a lower dimensional version of string/gauge duality, but here he uses not string theory on AdS3, but a quantum field theory. In a question afterwards, someone asked about string theory, and Witten just noted that perhaps what he had to say could be embedded in string theory, and that the recent Green et. al. paper showing that one can’t get pure supergravity by taking a limit of string theory did not apply in 3d. If one wants to interpret this new work in light of the the LQG/string theory wars, it’s worth noting that the technique used here, reexpressing gravity in terms of gauge theory variables and hoping to quantize in these variables instead of using strings, is one of the central ideas in the LQG program for quantizing 3+1d gravity. Witten was careful to point out though that there was no 3+1d analog of what he was doing, claiming that one can’t covariantly express gravity in terms of gauge theory in 3+1d (he said that LQG does this non-covariantly).

For negative Λ the theory has so-called BTZ black hole solutions, discovered by Banados, Teitelboim and Zanelli back in 1992, and it is for the quantum theory of these black holes that Witten is trying to find an exact solution. The technique he uses is one that goes back to the 80s, that of re-expressing the theory in terms of SO(2,1) (or its double cover SL(2,R)) gauge theory, where the action becomes the Chern-Simons action. More precisely, the Einstein-Hilbert action

$$I_{EH}=\frac{1}{16\pi G}\int d^3x\sqrt{g}(R +2/l^2)$$

(here the cosmological constant is $\Lambda=-1/l^2$) gets rewritten as an SO(2,2)=SO(2,1)XSO(2,1) gauge theory with connection

$$A= \begin{pmatrix}\omega & e \\ -e & 0 \end{pmatrix}$$

where &\omega; is a 3X3 matrix (the spin-connection), e is the 3d vielbein, and the gauge theory action is the Chern-Simons action

$$I=\frac{k^\prime}{4\pi}\int Tr(A\wedge dA+\frac{2}{3}A\wedge A\wedge A)$$

with $k^\prime=\frac{l}{4G}$ (that 4 may not be quite right…).

Witten wants to exploit the relation between this kind of topological QFT and 2d conformal field theory that he first investigated in several contexts (including one that won him a Fields medal) back in the late eighties. He notes that in this context the existence of left and right Virasoro symmetries with central charges $c_L=c_R=\frac{3l}{2G}$ was first discovered by Brown and Henneaux back in 1986, and he refers to this discovery as the first evidence of an AdS/CFT correspondence. If one really does have a CFT description, one expects that the central charges can’t vary continuously, but that 2+1d gravity will only make sense for certain values of $l/G$, but Witten notes that there is no rigorous way to find the right values one will get upon quantization.

He then goes on to make a “guess”, adding to the action a multiple of the Chern-Simons invariant of the spin connection

$$I^\prime=\frac{k}{4\pi}\int Tr(\omega\wedge d\omega + \frac{2}{3}\omega\wedge\omega\wedge\omega)$$

Now the theory depends on two parameters: $l/G$ and an integer k.

Using the fact that SO(2,2)=SO(2,1)XSO(2,1), one can rewrite the total action as the sum of two Chern-Simons terms

$$I= \frac{k_L}{4\pi} \int Tr(A_-\wedge dA_-+\frac{2}{3}A_-\wedge A_-\wedge A_-)$$
$$ \ \ + \frac{k_R}{4\pi}\int Tr(A_+\wedge dA_++\frac{2}{3}A_+\wedge A_+\wedge A_+)$$

for connections

$$A_{\pm}=\omega\pm e$$

Now instead of $l/G$ and k we have $k_L,k_R$ and these are quantized if we take the gauge theory seriously. By matching Chern-Simons and gravity the central charges turn out to be

$$ (c_L, c_R)= (24k_L, 24k_R)$$

and holomorphic factorization is possible in the 2d CFT for just these values

Looking at just the holomorphic part, we have a holomorphic CFT with central charge c=24k and ground state energy -c/24=-k (note, now a different k than before…).

The partition function is expected to be ($q=e^{-\beta}$)
$$Z(q)=q^{-k}\Pi_{n=2}^\infty \frac{1}{1-q^n}$$
The first term in the product is the ground state (AdS3), the only primary state, with the other terms Virasoro descendants (excitations of the vacuum from acting with the stress-energy tensor and derivatives).

Witten then goes on to note that this expression is not modular invariant, so one expects other terms in the product, corresponding to other primary states. By an argument I didn’t understand he claimed that these would be of order $q^{1}$, at an energy k+1 above the ground state, and his proposal was that it would be this modular invariant function that would include black hole states.

In these units the minimum black hole mass is M=k, but here one is getting states only at mass M=k+1 and above. This is because the Bekenstein-Hawking entropy of the M=k black hole is 0, so it doesn’t contribute to the partition function.

Witten claimed that this proposal gives degeneracies of states that agree with the Bekenstein-Hawking entropy formula. As an example, for k=1 the partition function is given by the famous J-function

$$J(q)=j(q)-744=q^{-1}+196884q+\ldots$$

and thus for a black hole of mass 2 the number of primaries is 196883 and the entropy is ln(196883)=12.19, which can be compared to the Bekenstein-Hawking semi-classical prediction of 12.57 (one only expects agreement for large k,M).

The number 196883 is famous as the lowest dimension of an irreducible representation of the monster group, and this partition function is famous as having coefficients that give the dimensions of the other irreducibles (“modular moonshine”). There is a conjecture that there is a unique CFT with this partition function. If so, it must be the CFT that has the monster group as automorphism group. It has always seemed odd that this very special CFT didn’t correspond to a particularly special physical system, but if Witten is right, now it has an interpretation in terms of the quantum theory of black holes in 2+1 dimensions.

Anyway, that’s what I was able to understand of what Witten had to say and what he was claiming. Other people have worked on this problem in the past, for a recent review article on this topic by Carlip, see here. Carlip describes the understanding of the problem at the time as “highly incomplete”, and one of the explanations he describes relates the black hole problem to the Liouville theory. A question from the audience after the talk asked about this, and Witten indicated that he thought the Liouville theory explanation did not work.

I’m no expert here, so unclear on the details, why some of these things might be true, and what the implications might be, but this does seem to be a remarkable new idea, involves beautiful mathematics, and seems to provide promising insight into a crucial lower dimensional toy model. I suspect it will draw a lot of attention from theorists in the future.

For this posting, I especially encourage any comments from people more knowledgable than myself who can correct anything I’ve got wrong. I also strongly discourage people who know little about this from contributing comments that will add noise and incorrect information. Bad enough that I’m trying to provide information about something I’m not expert on; if you can help that’s great, but if not, please don’t make it worse…

Update: Lubos has picked up on this, which he describes as having been “leaked”, and gives the usual argument that this must be part of string theory.

Posted in Favorite Old Posts, Uncategorized | 29 Comments

All Sorts of Stuff

Posted on May 5, 2007 by woit

For up-to-the-minute news about the Higgs, far better informed than any media source could ever be (and thus a great example of why blogs are changing the way the media works), your best bet is Tommaso Dorigo’s blog. His latest posting explains well what the current state is, and predicts that, with the data expected from the Tevatron through 2009, they should be able to have 2.5-3 sigma evidence for a 115 GeV Higgs if it is there, or if it’s not, rule it out at 95% confidence level up to 130 GeV. He shows a recent plot from D0 based on 1 fb-1 of data, and discusses the fact that D0’s limits on a Higgs are not quite as good as expected at low mass. When similar data from his own experiment (CDF) becomes available, it will be interesting to compare the results. Not being able to rule out a low-mass Higgs at the expected level probably just means that it’s harder to do than expected. But there’s another possible interpretation: maybe there’s something there….

Tommaso also has a posting about a new Physics World article discussing the recent blog-centered discussion of statistically-not-very-significant sightings of a possible new particle that could be a supersymmetric Higgs. Evidently these events have caused some consternation within CDF and D0 about the possible implications of bloggers in their midst and how this changes communication of their results to the public.

This month’s Blog Life column in Physics World covers Not Even Wrong, accurately and well.

On the mathematical side of things, Terry Tao continues to come up with amazingly good blog entries. His latest is a series of three postings (here, here and here), reporting on my colleague Shouwu Zhang’s lectures at UCLA on the topic of rational points on curves. This is a fundamental issue in number theory and arithmetic geometry, and the fact that Tao is a great mathematician, but not an expert, may have a lot to do with why his explanation of Shouwu’s lectures is relatively easy to follow. One of the problems with academia is that one’s illustrious colleagues (like Shouwu) get invitations to give lecture series like this elsewhere, but not at their home institutions. So, while I didn’t get to hear Shouwu’s lectures, Tao’s account of them is excellent compensation.

For an interesting article by a young philosopher about the question of beauty in physics, see this article in Perspectives in Science (based on his doctoral dissertation).

On May 22 the CUNY Graduate Center program on Science and the Arts will host an event entitled String Theory for Dummies. Unfortunately I’ll be out of town that day…

A couple weeks ago there was a workshop in Tel Aviv and Jerusalem on String Theory: Achievements and Perspectives, honoring the sixtieth birthday of Eliezer Rabinovici and Shimon Yankielowicz. Videos and some transparencies from the talks are available here. Susskind gives his usual propaganda for the anthropic string landscape, but seems rather defensive, starting off saying that he “feels like he’s at the center of a circular firing squad” (which maybe does describe what is going on in string theory these days), and that “some people say I’m a traitor” or that “my ideas are dangerous.”

Gross ended the conference with a remarkable discussion of the current state of string theory. He put up various cartoons illustrating the fact that the public perception of string theory has turned rather negative (including the recent one from the New Yorker: “Is String Theory Bullshit?”), but took solace in a recent use of string theory in an advertisement for women’s bikinis. He declared that “I am still a true believer in the sexiness of string theory”, and that he continued to think it is clearly on the right road. But, after giving the standard list of string theory achievements, he did admit that he was much less optimistic than 20 years ago, and spent some time discussing what he sees as the main failure to date: the continuing lack of a fundamental dynamical principle behind string theory. The question “what is string theory?” still has no real answer, and he has “the very uneasy feeling that we’re missing something big, that semi-classical intuition fails”, and that this will make the landscape disappear. Perhaps most remarkably, Gross admitted to some discouragement about AdS/CFT. He noted that the recent Klebanov et. al. results promoted by press release as connecting string theory with physics were actually due to an impressive gauge theory calculation. According to him, what has happened is that gauge theory techniques have proved more powerful than string theory techniques. He went on to discuss the landscape, explaining that he found the anthropic principle impossible to falsify, completely against the way physics has made progress in the past, and just “an easy way out”. Gross ended his talk by pointing out that 90 percent of the conference talks used supersymmetry, and that currently there was a “really weird situation”: supersymmetry was an essential tool, but there was absolutely no evidence for it. He said that he continues to believe that supersymmetry will be found at the LHC and has been willing to take 50/50 bets on the subject for bottles of wine, etc.

I haven’t yet had time to listen to many of the other talks, it looks like there are quite a few worth listening to, although as usual recently a depressingly large amount of landscape-based rather philosophical and pseudo-scientific argumentation.

I spent Thursday out at Stony Brook at the celebration of the 40th birthday of the ITP. It was great to catch up with many people I haven’t seen in nearly twenty years, hear what a lot of ex-Stony Brook people are doing, and meet some interesting new people (including some blog readers!).

Yesterday I spent much of the day downtown at the headquarters of the New York Academy of Sciences, which was hosting this semester’s Northeast String Cosmology Meeting, organized by Brian Greene and others from Columbia. The setting was pretty amazing, up on the 40th floor of the new 7 World Trade Center building, which has a spectacular view of lower Manhattan. Richard Bond gave a talk on topics concerning inflation and the CMB. He ended with lots of detailed calculations of CMB effects due to cosmological models involving string theory compactifications, especially a “Roulette Inflation” model. The joke was that God does not just play dice with the universe, but roulette also. In the question period Neil Turok politely pointed out that he was randomly choosing initial conditions, and getting very different imprints on the CMB, so wasn’t really able to predict anything. Nima Arkani-Hamed spoke on “Quantum Horizons and the Landscape”, talking about very general philosophical issues of horizons in AdS, the landscape, whether there are any “sharp observables” in this context and associated limits on the applicability of effective field theory. He ended by claiming that the situation is like that of the quantum theory in 1911, with the angst people are experiencing due to the landscape just like the difficulties physicists faced early in the century in going from classical physics to quantum physics. He didn’t mention that the old quantum theory was making lots of verified experimental predictions, whereas he is giving talks on whether, even in principle, the landscape can predict anything. Seems kind of different to me.

Among the many people there was Alan Guth, who, according to this blog entry someone pointed me to, has started “to have been converted over to thinking that anthropic arguments might have some merit.”

While I found these two talks depressing and all too symptomatic of the sad state of this subject, there was a huge bright spot at the workshop. Witten gave a really amazing talk about 2+1 d gravity. He has some fascinating new ideas about this, but they deserve a completely separate posting, which I’ll try to get to writing up tomorrow…

Posted in Uncategorized | 9 Comments