Not Even Wrong

David Gross just finished giving the closing talk at Strings 2008, on the outlook for string theory, following a talk by Hirosi Ooguri summarizing the conference. Strings 2009 will be in Rome next June, and it appears that there is a tentative plan to have Strings 2010 in College Station, Texas.

Gross began his talk by recalling his days as a postdoc at CERN in the late 60s, working on an early version of string theory (e.g. trying to extend the Veneziano model). At the time he felt CERN was a great center of theory, but somewhat of an experimental backwater, with the real action he was interested in happening at SLAC. Now, forty years later both string theory and CERN have flourished. CERN is in the process of becoming the single world umbrella lab doing particle physics, driving all the others out of business. Unfortunately, Gross sees the same thing happening in particle theory and seems rather pleased about it, saying that only one umbrella in theoretical physics will survive, string theory, eating up everything else. Except LQG, which he says has not yet been brought under the umbrella, and “we’re not sure we want to”.

I found this display of string theory triumphalism truly appalling. The fact of the matter is that string theory has failed miserably to do what it was supposed to do, explain unexplained features of the standard model and predict what happens beyond it. Under the circumstances, to claim victory and write out of particle theory anything that doesn’t fit under the string theory “umbrella” is completely inappropriate. The message to any young particle theorist from Gross was clear: fall in line with string theory ideology, or there will be no place for you under the “umbrella”, i.e. no job for you (the phenomenologists have their own umbrella, you better try that one). The fact that HEP experiment is being forced to consolidate in one lab by economic realities is a really unfortunate one. There is no similar reason for HEP theory to be forced to consolidate around one topic.

Later on in the talk, Gross started channeling Lee Smolin and me, urging young people to stop sticking to the same well-worn ideas, to stop looking under the same lampposts, and to go out and search for something really new. He argued that they would find wandering in the darkness less competitive since few people were doing it. It was unclear whether one is allowed to get out from under the umbrella when one goes out to investigate the darkness, presumably not.

While he made lots of positive comments about current work in string theory in order to rally the troops, much of his talk was rather pessimistic and critical of trends in string theory research. He acknowledged that there hadn’t been any “great breakthroughs” in the field in quite a while. String phenomenology was described an attempt to make string theory “a predictive, or at least imitative” framework. He didn’t comment on what it means for theorists to give up on predicting nature, and settling for imitating it.

About the LHC, he acknowledged that it is unlikely to have anything to say about string theory. He finds the idea of seeing black holes, strings, etc. “extremely unlikely”, but is betting that the Higgs and supersymmetry will show up. Unfortunately, even if supersymmetry is found “it’s not clear that we’re going to learn enough”, this won’t answer any deep questions about string theory or prove that it is relevant. His “most optimistic hope” is that the LHC will see something unexpected, and “we will realize that this was an obvious prediction of string theory”. He notes that this is “almost our last chance”, if nothing relevant to string theory shows up at this energy scale, it is unlikely that anything relevant will show up at any energy scale accessible for an extremely long time.

Gross commented on two topics that hadn’t been mentioned in the talks. He’s still hoping for a non-anthropic explanation of the CC, and noted that no speaker had brought up the anthropic landscape explanation of the CC, with it getting a mention only at one after-dinner talk. Despite what Susskind claims, perhaps the battle between the anthropicists and their opponents is not going so well for the anthopic side. They may get pushed out from underneath the umbrella…

The second topic was the still unsolved question of “what is string theory?”. Gross noted that there were no talks on string field theory, since it and most other ideas about how to define string theory non-perturbatively have gone nowhere. The one thing that is still alive is AdS/CFT, which now completely dominates the subject. More and more, particle theory research under the umbrella is focused only on things related to the duality of N=4 SSYM and string theory on AdS⁵ x S⁵. Gross noted the progress toward showing this duality, with the planar limit perhaps being done within the next few years.

By the way, in Ooguri’s talk, he mentions an AdS/CFT discrepancy that has been resolved, saying he was surprised that some blogger didn’t claim this discrepancy as disproof of AdS/CFT. Lubos in his commentary helpfully explains that Ooguri was referring to “numerous pigs and Woits”. Since I’ve never argued that there’s a problem with AdS/CFT duality, I guess he must be talking about someone else. Maybe Jacques Distler has some postings about problems with AdS/CFT that I missed.

Gross takes the attitude that there is no more value in working on “tests” of AdS/CFT, that the conjecture is now well-tested and it is time to move on to try and understand what AdS/CFT is good for, especially what it says about the question of “what string theory is?”. The planar limit is just the classical limit, and he discusses prospects for moving beyond it [and beyond AdS/CFT, to other backgrounds]. On the QFT side, this means deforming the gauge theory by non-renormalizable operators, so it is not clear what to do.

Update: More summary commentary and prizes at Resonaances. Clifford Johnson watched Gross’s talk and summarizes it as follows:

David Gross summed it all up, took stock of where we are, and where we aren’t, and looked forward. A sort of “state of the union” speech if you like. And the state is good. Very good indeed.

Dan Freed has a wonderful preprint out on the arXiv this evening, based on a talk he gave at the celebration of MSRI’s 25th anniversary, entitled Remarks on Chern-Simons Theory. It’s mainly about the current state of attempts to better understand the mathematical significance of the Chern-Simons-Witten quantum field theory.

This is a truly remarkable and very simple 3d quantum gauge theory, the significance of which Witten first came to understand back in 1988. He quickly showed that the theory brought together in an unexpected way several quite different but important areas of mathematics and physics (3d topology, moduli spaces of vector bundles, loop group representations, quantum groups, 2d conformal field theory among others). This work was the main reason he was awarded a Fields medal in mathematics in 1990. While Witten and others worked out many important aspects of this story back then, many important puzzles still remain, and it is these that Freed concentrates on.

Perhaps the biggest puzzle is that of how to actually define the theory in a local manner. The standard definition thrown around is that this is just the QFT with Lagrangian given by the Chern-Simons number CS[A] of a connection A, so all one has to do is evaluate the path integral
$$\int [dA] e^{i2\pi k CS(A)}$$
While this is a good starting point for a perturbative expansion at large k, it doesn’t appear to make much sense non-perturbatively. Freed points out that it is known that the theory must depend on additional topological structure on the 3-manifold (e.g. a 2-framing), whereas the path integral looks like it only depends on the orientation. If you try and think about how you would actually calculate such an integral numerically, by discretizing it and taking a limit, it looks like you will end up with something hopelessly dependent on the details of the discretization and the limit. For a much simpler toy example with some of the same problems, consider the path integral on closed curves on a sphere, taking as Lagrangian the enclosed area.

Freed describes in detail the state of attempts to rigorously define the theory without dealing with the path integral, but instead exploiting the fact that it is supposed to be a topological qft, and thus may have an abstract definition in terms of generators and relations. He describes the current situation as follows:

There is a generators-and-relations construction of the 1-2-3 theory via modular tensor categories for many classes of compact Lie groups G. This includes finite groups, tori, and simply connected groups, the latter via quantum groups or operator algebras.

There are new generators-and-relations constructions – at this stage still conjectural – of the 0-1-2-3 theory for certain groups, including finite groups and tori.

There is an a priori construction of the 0-1-2-3 theory for a finite group.

There is an a priori construction of the dimensionally reduced 1-2 theory for all compact Lie groups G

The bottom line is that we only have a local construction of the theory for the case of finite groups, where one can make perfectly good sense of the path integral. For the case of a 3-manifold that is a product of a circle and a Riemann surface, one can define things in terms of a 2d theory, and Freed explains the connections to the Freed-Hopkins-Teleman theorem.

To convince mathematicians that there is something to the path integral, Freed writes down the asymptotic expansion for large k that it leads to, and shows that this gives a highly non-trivial conjecture relating quite different mathematical objects associated with a 3-manifold. He shows strong numerical evidence for this conjecture.

Finally, he ends with some extensive and interesting comments about the relationship between quantum field theory and mathematics, as it has been pursued by both physicists and mathematicians over the past quarter-century, with some speculation about what direction this might take in the future.

The current plan at CERN is to celebrate my birthday by trying to circulate the first beam around the LHC on September 10 (actually my birthday is September 11, but in recent years my family, like CERN, has tended to celebrate on the 10th, feeling that 9/11 has too unfortunate connotations). One can follow this at a special web-site set up by CERN called LHC First Beam, which now is running a daily countdown.

String theorists have been flocking to CERN this summer trying to somehow connect their subject with the LHC. The big yearly Strings 08 conference will be starting there next week. The organizers don’t seem to have a lot of sympathy for anthropic pseudo-science, with no talks scheduled on anthropics, the landscape, or the multiverse. Instead they’ll be wisely sticking mostly to talks on topics related to better understanding more formal issues in string theory and quantum field theory.

In the weeks leading up to the conference though, CERN is hosting a theory institute on String Phenomenology. The web-site of the institute has a section on its “Scientific Case”, which, with remarkable chutzpah makes the claim that:

… the past few years have provided a drastic improvement on the potential for string theory models to be confronted with low-energy data

a claim that is diametrically opposed to reality.

For a look at the reality of what the landscape has meant for the “potential for string theory models to be confronted with low-energy data”, one can take a look at the slides of talks by Wati Taylor and Michael Douglas. Taylor describes the importance of distinguishing two possibilities he calls A (anything goes) and B (constraints), and finds in IIA intersecting brane models that the evidence favors A. It seems that such a landscape can give one pretty much any kind of low energy physics, with the things one can compute (the gauge group and number of generations) randomly and independently distributed. He looks for some hope in cosmology, noting that a large class of IIA models are incompatible with slow-roll inflation, while at the same time also pointing out that there are lots of potential ways around this particular constraint, although most of them involve uncontrolled approximations.

Douglas’s talk was entitled String Landscape: A Status Report, and in it he describes evidence for the existence of order 10⁵⁰⁰ “quasi-realistic vacua”. If you don’t impose some constraints from experiment, you’d have an infinite number of possible vacua. He claims that there is no way to rule out any of these vacua, other than to try and compute detailed predictions of each one (something no one has a clue about how to do). Douglas explained why it isn’t possible to make even the crudest prediction that initially he and others had hoped for, that of whether the SSYM breaking scale would be at observable or Planck energies. There’s an odd speculative section about how since SU(2) and SU(3) have shown up on energy scales of 100 MeV to 100 GeV, maybe one gets two new gauge groups for every factor of 1000 in energy (which he calls the “jungle scenario”, as opposed to the conventional “desert scenario”). There’s a final “No Conclusions” section, admitting that “at this point it seems likely that we will not have definite conclusions of predictions before LHC data comes in.” He ends with the standard piece of wishful thinking that now is all that is left of the project of connecting string theory unification models with physics:

Let us hope that discoveries here at Cern will reveal enough about the real world to make contact [with string theory] possible.

Yesterday there was a discussion session on “the string theory landscape and its impact on particle physics and cosmology”, but it doesn’t appear to be online. I wonder what conclusions the participants reached…

Update: Jester at Resonaances has a posting up about this. His impression of the Vafa et al. recent claims about “F-theory phenomenology” seems to match mine:

For the neutrino physicists the important piece of information is that the neutrinos are Dirac or Majorana and their masses are roughly of the order of what is observed. I heard some sceptics saying that back in the old days phenomenology meant a different thing, but such grumbling should not be taken seriously.

Alexander Grothendieck’s 80th birthday was this past March, and the September Notices of the AMS has several articles about his later years. There’s a long piece entitled Who is Grothendieck?, by Winfried Scharlau, who is writing a three-volume biography. The first volume (in German) is available here and mainly deals with the stories of his parents. The article contains the only pictures I’ve ever seen of the post 1970s Grothendieck and a wealth of information about his activities after leaving the mathematical research world.

The same issue contains a short piece Memories of Shourik, by Valentin Poenaru reminiscing about his friendship with Grothendieck during the 1960s. The most shocking thing in it to me was actually the part about Barry Mazur’s wife, who Poenaru describes as being only 17 when he met her living with Mazur at Bures-sur-Yvette.

Note added: Mazur’s biography here mentions just one wife, Grace Dane, a Harvard biology postdoc he married in 1960. If she was, as Poenaru claims, 17 in 62-63, that would have made her a 15 year-old postdoc when they married….

Finally, there’s a piece by Allyn Jackson about Grothendieck and the IHES, which is having its 50th birthday this year. Evidently Grothendieck has recently been in communication with the IHES:

Six months to the day before the start of the IHES anniversary celebration, Grothendieck wrote to the institute with a request for books. The IHES sent him the books as quickly as it could. But the exchange of letters between Grothendieck and the IHES administration culminated in his writing a furious “open letter” recounting his view of the exchange, which he took as deeply insulting towards him. He requested that copies of the open letter be sent to all members of the IHES Scientific Council and explicitly states that this letter is public (though he also says he will make no efforts on his own to publicize it). Having seen the open letter, I can say that it conveys an extreme outrage that indicates how difficult it would be to conduct reasonable communication with him.

At the same time, the open letter reveals the vivid personal tie that Grothendieck clearly still feels to the IHES. The letter also reveals an isolated individual who is reaching out in the only way he is able. In one place he speaks of his open letter as being a letter of farewell (“adieu”) to a world with which he no longer has anything in common. He ends on a note of apocalyptic foreboding, saying “that the time is near when…this letter, this cry will be known by all. In a world of the living.” This cry does not seem to concern misunderstanding over his original request for books. Rather, it speaks of anguish in the heart of one of the great mathematicians of modern times.

The IHES is having Recoltes et Semailles, Grothendieck’s long meditation on mathematics and his withdrawal from it, published this summer. Articles about this are beginning to appear in the French press, see here and here.

Things don’t seem to be going well these days for string theory in the “marketplace of ideas”. From an article about gasoline-saving pedals:

The 1990’s were the host of many great fads. Furby, Tamagachis, string theory, the examples are as numerous as the many incarnations of Prince.

Today’s “Science Saturday” on Bloggingheads features me and Sabine Hossenfelder, supposedly talking about What’s wrong with string theory. Actually, we both agreed that we were pretty tired of that topic, so tried to discuss some more interesting related issues we both have an interest in. Here’s a clip from the full thing, I promise to not start regularly embedding video in this blog:

I hope this thing came out all right. It was recorded a couple weeks ago, in a process involving no trouble on my end, but heroic efforts on Sabine’s. While Sabine had to set the whole thing up on her end, and ended up crouched in an attic since it was the only place she could get a connection of good enough quality, I just sat at my office chair and someone from Bloggingheads took care of everything. Unfortunately we couldn’t see each other while talking. I can’t really bear the thought of watching myself on video, so I guess I’ll never see exactly how this turned out, but I’m glad to see that the turtles on the bookcase behind me made it into the frame.

Sabine has her own posting about this here, and the full thing is here.