Frenkel on String Theory

Curt Jaimungal’s Theories of Everything podcast has a new episode featuring a long talk with Edward Frenkel (by the way, I’ll be doing one of these next month). A few months ago I wrote about a Lex Fridman podcast with Frenkel here. While both of these are long, they’re very much worth watching.

While there’s some overlap between the two podcasts, some different topics are covered in the new one. In particular, one thing that happened to Frenkel since last spring is that he attended Strings 2023 and gave a talk there (slides here, video here). The experience opened his eyes to just how bad some of the long-standing problems with string theory have gotten, and starting around here in the podcast he has a lot to say about them.

It’s pretty clear that his reaction to what he saw going on at the conference was colored by his experience growing up in late Soviet-era Russia, where the failure of the system had become clear to everyone, but you weren’t supposed to say anything about this. He pins responsibility for this situation on senior leaders of the field, who have been unwilling to admit failure. As part of this, he acknowledges his own role in the past, in which he was often happy to get some reflected glory from string theory hype by playing up its positive influence on parts of mathematics while ignoring its failure as a theory of the real world. In any case, I urge you to watch the entire podcast, it’s well worth the time.

For a very different perspective on the responsibility of senior people for string theory’s problems, you might want to take a look at the bizarre twitter feed of stringking42069, which may or may not be some very high-quality trolling. In between replies and tweets devoted to weightlifting, weed and women, the author has some very detailed and mostly scornful commentary on the state of the field and the behavior of its leaders. His point of view is that the leaders have betrayed the true believers like himself, abandoning work on the subject in favor of irrelevancies like “it from qubit”, in the process tanking the careers of young people still trying to work on actual string theory. For a summary of the way he sees things, see here and here. Comments on specific people here and here.

This weekend here in New York if you’ve got $35 you can attend an event bringing together five of the people most responsible for the current situation. I doubt that the promised evaluation of “a mathematically elegant description that some have called a “theory of everything.”” will accurately reflect the state of the subject, but perhaps some of the speakers will have listened to what Edward Frenkel has to say (or read stringking42069’s tweets) and realized that a new approach to the subject is needed.

Update: Curt Jaimungal at the Theories of Everything podcast has a new episode, discussing quantum gravity with Jonathan Oppenheim. Around 1:10 Oppenheim has some comments about the current problem of few opportunities for young people to pursue new ideas in this field, including:

You know, it’s a multifaceted problem. I think part of it is that for whatever reason, people like to work on the same thing as everyone else. And I mean, we are social creatures, and we want to be part of the community. And so if there’s a big community doing something, then it’s very natural to want to be part of that community and do that research.

But it’s, I feel like it’s gotten to quite an extreme. It feels quite extreme at the moment, I feel like even when I was a student, you know, there were various researchers who, I would say, didn’t have a firm allegiance to say, string theory or loop quantum gravity, and you could kind of work with one of them and work on your own approach. Whereas I think now, for whatever reason, the landscape has just become a lot more divided into different communities who do different things, and it’s much harder to go off on your own. And maybe that’s just because it’s students worry that if they go off on their own, they won’t get a job. I think that’s probably a big part of it.

Update: Bringing together this and the last posting, if you’d like more Frenkel and more Langlands, there’s a new Numberphile video out.

Posted in Uncategorized | 27 Comments

What Does Spec Z Look Like?

This week Laurent Fargues has started a series of lectures here at Columbia on Some new geometric structures in the Langlands program. Videos are available here, but unfortunately there is a problem with the camera in that room, making the blackboard illegible (maybe we can get it fixed…). Fargues however is writing up detailed lecture notes, available here, so you can follow along with those.

Fargues is covering the story of the Fargues-Fontaine curve and the relationship between geometric Langlands on this curve and arithmetic local Langlands that he worked out with Scholze recently. On Monday Scholze gave a survey talk in Bonn entitled What Does Spec Z Look Like?, video available here. Scholze’s talk gave a speculative picture of how to think about the global arithmetic story, with Spec Z as a sort of three-dimensional space. One thing new to me was his picture of the real place as a puncture, with boundary the twistor projective line. He then went on to motivate the course he will be teaching this fall with Dustin Clausen on Analytic Stacks. Here at Columbia we have an ongoing seminar on some of the background for this, run by Juan Rodriguez Camargo and John Morgan.

Update: Peter Scholze next week at the Rapoport conference will be giving a talk on new ideas about the twistor $$\mathbf{P}^1$ and real local Langlands. His abstract is

Towards a formulation of the real local Langlands correspondence as geometric Langlands on the twistor-$\mathbf P^1$

We will propose a formulation of the local Langlands correspondence for complex representations of real groups in terms of a(n everywhere unramified) geometric Langlands correspondence on the twistor-$\mathbf P^1$, analogous to our work with Fargues in the case of p-adic groups. This is motivated by discussions with Rodriguez Camargo, Pan, le Bras and Anschütz on the analogous case of locally analytic p-adic representations, and is different from the previous work of Ben-Zvi and Nadler in a similar direction. In particular, on the geometric side we get representations of the real group, encoded in terms of liquid quasicoherent sheaves on $[*/G(\mathbf R)^{la} ]$; and on the spectral side, we get representations of the real Weil group $W_R$, or rather vector bundles on $[(\mathbf A^2\backslash\{0\})/W_R^{la} ]$.

Posted in Langlands | 23 Comments

Various and Sundry

The math department at Columbia this fall will be hosting three special lecture series, each with some connection to physics (at least in my mind…):

Some other less inspirational topics:

  • The news this summer from the LHC has not been good. On July 17 a tree fell on two high-voltage power lines, causing beams to dump, magnets to quench, and damage (a helium leak) to occur in the cryogenics for an inner triplet magnet. See here for more details. Fixing this required warming up a sector of the ring, with the later cooldown a slow process. According to this status report today at the EPS-HEP2023 conference in Hamburg, there will be an ion run in October, but the proton run is now over for the year, with integrated luminosity only 31.4 inverse fb (target for the year was 75).
  • The Mochizuki/IUT/abc saga continues, with Mochizuki today putting out a Brief Report on the Current Situation Surrounding Inter-universal Teichmuller Theory (IUT). The main point of the new document seems to be to accuse those who have criticized his claimed proof of abc of being in “very serious violation” of the Code of Practice of the European Mathematical Society. This is based upon a bizarre application of the language

    Mathematicians should not make public claims of potential new theorems or the resolution of particular mathematical problems unless they are able to provide full details in a timely manner.

    to the claim by Scholze and Stix that there is no valid proof of the crucial Corollary 3.12. It would seem to me that Mochizuki is the one in danger of being in violation of this language (he has not produced a convincing proof of this corollary), not Scholze or Stix. The burden of proof is on the person claiming a new theorem, not on experts pointing to a place where the claimed proof is unsatisfactory. Scholze in particular has provided detailed arguments here, here and here. Mochizuki has responded with a 156 page document which basically argues that Scholze doesn’t understand a simple issue of elementary logic.

    Also released by Mochizuki today are copies of emails (here and here) he sent last year to Jakob Stix demanding that he publicly withdraw the Scholze-Stix manuscript explaining the problem with Mochizuki’s proof. Reading through these emails, it’s not surprising that they got no response. The mathematical content includes a long section explaining to Scholze and Stix that the argument they don’t accept is just like the standard construction of the projective line by gluing two copies of the affine line. On the topic of why he has not been able to convince experts of the proof of Corollary 3.12, Mochizuki claims that he convinced Emmanuel Lepage and that

    one (very) senior, high-ranking member of the European mathematical community has asserted categorically (in a personal oral communication) that neither he nor his colleagues take such assertions (of a mathematical gap in IUT) seriously!

    I suppose this might be Ivan Fesenko, but who knows.

  • Since the Covid pandemic started, the World Science Festival has not been running its usual big annual event here in New York. This fall they will have an in-person event, consisting of four days of discussions moderated by Brian Greene. In particular there will be a panel Unifying Nature’s Laws: The State of String Theory evaluating the state of string theory, featuring four of the most vigorous proponents of the theory (Gross, Strominger, Vafa and Witten). I suspect their evaluation may be rather different than that of the majority of the theoretical physics community.

Update: Quanta has a very good article by Kevin Hartnett about the telescope conjecture in homotopy theory and its recent disproof. This is due to work of Ishan Levy, Robert Burklund, Jeremy Hahn and Tomer Schlank, all of whom gave talks on the subject at the Oxford conference this past June in honor of the 65th birthday of Mike Hopkins. Videos of the talks are available here. If homotopy theory is not your thing, and if you haven’t heard Graeme Segal speak recently about his thinking on the definition of quantum field theory, you could instead watch his talk.

: Video of Klainerman’s lectures will be available here:

Posted in abc Conjecture, Uncategorized | 13 Comments

The Philosophy of Supersymmetry

A few months back I saw a call for papers for a volume on “Establishing the philosophy of supersymmetry”. For a while I was thinking of writing something, since the general topic of supersymmetry is a complex and interesting one, about which there is a lot to say. Recently though it became clear to me that I should be writing up other more important things I’ve been working on. Also, taking a look back at the dozen or so pages I wrote about this 20 years or so ago for the book Not Even Wrong, there’s very little I would change (and I’ve written far too much since 2004 about this on the blog). What follows though are a few thoughts about what “supersymmetry” looks like now, maybe of interest to philosophers and others, maybe not…

First the good: “symmetry” is an absolutely central concept in quantum theory, in the mathematical form of Lie algebras and their representations. Most generally, “supersymmetry” means extending this to super Lie algebras and their representations, and there are wonderful examples of this structure. A central one for representation theory involves thinking of the Dirac operator as a supercharge: by extending a Lie algebra to a super Lie algebra, Casimirs have square roots, bringing in a whole new level of structure to familiar problems. In physics this is the phenomenon of Hamiltonians having square roots when you add fermionic variables, providing a “square root” of infinitesimal time translation.

Going from just a time dimension to more space-time dimensions, one finds supersymmetric quantum field theories with truly remarkable properties of deep mathematical significance. Example include 2d supersymmetric sigma models and mirror symmetry, 4d N=2 super Yang-Mills and four manifold invariants, 4d N=4 super Yang-Mills and geometric Langlands.

But then there’s the bad and the ugly: attempts to extend the Standard Model to a larger supersymmetric model. From the perspective of 2023, the story of this is one of increasingly pathological science. In 1971 Golfand and Likhtman first published an extension of the Poincaré Lie algebra to a super Lie algebra. This was pretty much ignored until the end of 1973 when Wess and Zumino rediscovered this from a different point of view and it became a hot topic among theorists. Very quickly it became clear what the problem was: the new generators one was adding took all known particle states to particle states with quantum numbers not corresponding to anything known. In other words, this supersymmetry acts trivially on known physics, telling you nothing new. It became commonplace to advertise supersymmetry as relating particles with different spin, without mentioning that no pairs of known particles were related this way. In all cases, a known particle was getting related to an unknown particle. Worse, for unbroken supersymmetry the unknown particle was of the same mass as the known one, something that doesn’t happen so the idea is falsified. One can try and save it by looking for a dynamical mechanism for spontaneous supersymmetry breaking and using this to push superpartners up to unobservable masses, but this typically makes an already pretty ugly theory far more so.

The seriousness of this problem was clear by the mid-late 1970s, when I was a student. The one hope was that maybe some extended supergravity theory with lots of extra degrees of freedom would dynamically break supersymmetry at a high scale, leaving the Standard Model as the low energy part of the spectrum. There wasn’t any convincing way to make this work, and it became clear that one couldn’t get chiral interactions like those of the electroweak theory this way. 1984 saw the advent of a different high scale model supposed to do this (superstring theory), but that’s another story.

Looking back from our present perspective, it’s very hard to understand why anyone saw supersymmetric extensions of the SM as plausible physics models that would be vindicated by observations at colliders. For example, Gross and Witten in 1996 published an article in the Wall Street Journal explaining that “There is a high probability that supersymmetry, if it plays the role physicists suspect, will be confirmed in the next decade.” Ten years later, when the Tevatron and LEP had seen nothing, the same argument was being made for the LHC. After over a decade of conclusive negative results from the LHC, one continues to hear prominent theorists assuring us that this is still the best idea out there and large conferences devoted to the topic. Long ago this became pathological science. In the call for papers, the issue is framed as:

recent debates on the prospects of low energy supersymmetry in light of its non-discovery at the LHC raise interesting epistemological questions.

From what I can see, the questions raised are not of an epistemological nature, but perhaps the philosophers will find a way to sort this out.

Update: There was a workshop on this last year, abstracts here.

Update: I happened to come across today this 2021 interview of Daniel Freedman by David Zierler. Zierler repeatedly asks Freedman why he has faith in SUSY despite the long history of no evidence. Near the end, Freedman gives this very defensive explanation:


What I hear in your remarks is an adherence to supersymmetry despite its immediate experimental prospects. Is that a belief or is it something more?


It’s a belief which stems from confidence in the powerful symmetry which underlies the subject. Some human beings indulge in beliefs which have no basis whatsoever. Some of those beliefs are destroying our society at the moment. My belief in a credible and interesting physical theory isn’t going to hurt anybody.

Posted in Uncategorized | 23 Comments

Strings 2023

For much of the past week, I’ve been attending off and on (on Zoom) the Strings 2023 conference. This year it’s in a hybrid format, with 200 participants in person at the Perimeter Institute, and another 1200 or so on Zoom. These yearly conferences give a good idea of what some of the most influential string theorists think is currently important, and I’ve been writing about them for twenty years. Videos of the talks are being posted here.

As in many of these Strings conferences in recent years, there was very little discussion of strings at Strings 2023. Of the 24 standard research talks, only 4 appeared to have anything to do with strings. A new innovation this year was to schedule in addition four “challenge talks”, conceived of as talks explicitly about material outside of string theory that might interest string theorists. In particular Edward Frenkel gave a nice survey of a wide range of ideas from quantum integrable systems and ending up with geometric Langlands. He motivated this with reference to what Feynman was working on very late in life and the problem of solving QCD. His slides are here, video here.

In addition there were four morning “Discussion Sessions”, which I attended most of, and at which string theory put in little to no appearance. Today’s discussion featured Nati Seiberg and Anton Kapustin and was about lattice versions of QFT, especially in their topological and geometrical aspects, a very non-stringy topic dear to my heart. Yesterday was It From Qubit, which had Geoff Penington discussing topics related to black holes. The conventional wisdom now seems to be that the information paradox is gone, solved semi-classically, so giving no insight into true quantum gravity dynamics. While this means you can’t see anything interesting at large distances from the black hole, Penington had some new ideas about something that might in principle be observable at atomic-scale distances from a super-massive black hole. Maldacena started off the session with slides promoting the way forward as quantum computer simulations involving 7000 qubits, a variant on the wormhole publicity stunt. The only time string theory made an appearance was in a suggestion by Dan Harlow that perhaps by doing quantum computer simulations theorists could solve the the problem of what “string theory” really is. It’s pretty clear what the leading direction is now for continuing the long tradition in string theory of outrageous hype.

After this week, I’m even more mystified about why the conference was called “Strings 2023” And how does one decide these days what “string theory” is and who is a “string theorist”? Oddly, two of the things that now distinguish this yearly conference from others are a pretty rigid exclusion of both real world physics (Frenkel comments on this here) as well as of what got people excited about string theory, superstring unification and its implications for seeing low energy SUSY at colliders. People still interested in that have split off to other conferences, especially String Phenomenology 2023 and SUSY 2023.
Those conference have their own kinds of mysteries (why do people keep working on ideas that failed long ago?). In particular, the closing talk on the Status and Future of Supersymmetry at SUSY 2023 was all about the great prospects for SUSY at the LHC, and included a Conclusion written (no joke) by ChatGPT:

The future of supersymmetry as a research program holds both exciting challenges and potential breakthroughs. While the LHC experiments have yet to observe direct evidence of supersymmetric particles, ongoing theoretical advancements and refined experimental techniques offer renewed hope. The future of supersymmetry research lies in two key directions. Firstly, novel theoretical models are being explored, including new variants of supersymmetry that incorporate dark matter candidates or non-linear realizations. These approaches push the boundaries of our understanding and allow for further exploration of the particle zoo. Secondly, upcoming experiments, such as the High-Luminosity LHC and future colliders, aim to explore higher energy scales and increase the sensitivity to supersymmetric signals. With these advancements, the quest for supersymmetry will continue to shape the field of particle physics, inspiring new theoretical insights and propelling experimental discoveries.

Things just get stranger and stranger…

Update: Speaking of stranger and stranger, you can listen here to Sean Carroll talking by himself for four hours and twenty-two minutes about why there really is no crisis in physics, the whole supersymmetry/string theory thing is going just fine.

Update: I hadn’t realized just how accurate Joe Conlon’s description of the conference as “IAS-centric” was. For the four discussion sections, no IAS in one of them (“strings, QFT and mathematics”, the other 3 sessions were all IAS (two IAS faculty, the rest an assortment of ex or current members).

Posted in Strings 2XXX | 18 Comments

This Week’s Hype

Nanopoulos and co-authors have predictions from superstring theory that are “in strong agreement with NANOGrav data.” He has been at this now for almost 40 years. See for instance Experimental Predictions from the Superstring from 1985, where the superstring predicted a top mass of 55 GeV and 360 GeV squarks.

Posted in This Week's Hype | 11 Comments

Understanding Confinement

This week and next there’s an interesting summer school going on at the IAS, with topic Understanding Confinement. Videos of talks are available here or at the IAS video site.

Taking a look at some of the first talks brings back vividly my graduate student years, which were dominated by thinking about this topic. When I arrived in Princeton in 1979, the people there had been working for several years on trying to understand confinement semi-classically, in terms of instantons and other solutions to the Yang-Mills equations (e.g. merons). By 1979 it had become clear that such semi-classical calculations were not sufficient to understand confinement and people were looking for other ideas. There were quite a few around, including the idea that there was some sort of string theory dual to pure Yang-Mills theory, and I spent quite a lot of time reading up on efforts of Migdal, Polyakov and others to find a formulation of string theory that would provide the needed dual. I ended up writing my thesis on lattice gauge theory, an approach which had the great advantage that you could at least put the calculation on a computer and start trying to get a reliable result for pure Yang-Mills numerically. Some of the calculations I did were done at the IAS, with Nati Seiberg and others. The other thing I spent a lot of time thinking about was how to put spinor fields on the lattice, the beginning of my interest in the geometry of spinors.

I strongly recommend watching Witten’s talk on Some Milestones in the Study of Confinement. His career started a few years before mine, with the early part very much dominated by the problem of how to make sense of Yang-Mills theory non-perturbatively, and this has has always been a motivating problem behind much of his work. In his talk he explains clearly the approaches to the problem (lattice gauge theory, 1/N, dual Meissner) that appeared very soon after the advent of QCD in 1973. He emphasizes how each of these approaches shows indications of a possible string theory dual, while frustratingly not leading to a string model that has the right properties, summarizing (41:30) the situation with:

The string theory we want is probably quite unlike any that we actually know, as of now. We don’t know how to make a string theory with the short distance behavior of asymptotic freedom.

In his talk he discusses later developments, in particular the Seiberg-Witten solution to N=2 SYM and the AdS/CFT duality between a string theory and N=4 SYM, explaining how these advances still don’t provide a viable approach to the confinement problem in pure Yang-Mills.

I’m looking forward to seeing the rest of the talks, and finding out more about some things that have happened over the years since I was most actively paying attention to what was happening with the confinement problem.

Posted in Uncategorized | 7 Comments

Relative Langlands Duality

For several years now, David Ben-Zvi, Yiannis Sakellaridis and Akshay Venkatesh have been working on a project involving a relative version of Langlands duality, which among many other things provides a perspective on L-functions and periods of automorphic forms inspired by the quantum field theory point of view on geometric Langlands. For some talks about this, see quite a few by David Ben-Zvi (for example, talks here, here, here and here, slides here and here), the 2022 ICM contribution from Yiannis Sakellaridis, and Akshay Venkatesh’s lectures at the 2022 Arizona Winter School (videos here and here, slides here and here). Also helpful are notes from Ben-Zvi’s Spring 2021 graduate course (see here and here).

A paper giving details of this work has now appeared, with the daunting length of 451 pages. I’m looking forward to going through it, and learning more about the wide range of ideas involved. A recent post advertised James’s Arthur’s 204 page explanation of the original work of Langlands, and the ongoing progress on the original number field versions of his conjectures. It’s worth noting that while there are many connections to the ideas originating with Langlands, this new work shows that the “Langlands program” has expanded into a striking vision relating different areas of mathematics, with a strong connection to deep ideas about quantization and quantum field theory. The way in which these ideas bring together number theory and quantum field theory provide new evidence for the deep unity of fundamental ideas about mathematics and physics.

Posted in Langlands | 4 Comments

Million Dollar Prize for Scholze and Stix

At a news conference in Tokyo today there evidently were various announcements made about IUT, the most dramatic of which was a 140 million yen (roughly one million dollar) prize for a paper showing a flaw in the claimed proof of the abc conjecture. It is generally accepted by experts in the field that the Scholze-Stix paper Why abc is still a conjecture conclusively shows that the claimed proof is flawed. For a detailed discussion with Scholze about the problems with the proof, see here. For extensive coverage of the IUT story on this blog, see here.

Between paywalls and the limitations of Google translate, I’m not sure exactly what the process is for Scholze and Stix to collect their million dollars. Perhaps they just need to publish their paper, but it seems that the decision may be up to the businessman who is contributing the funds, and it’s unclear what his process will be.

For a few sources I’ve found, see here, here and here. If others have reliable and more detailed sources they can point to (especially anything in English), please do so.

Update: Press release here. Rules for the million dollars are

Nobuo Kawakami makes his own judgment as an individual.
The review method will not be disclosed, but the papers to be reviewed must be papers in mathematics that have been published on MathSciNet and have published more than 10 papers on arithmetic geometry in the past 10 years. Only papers that have been peer-reviewed and published in journals.

Scholze and Stix may not want to take time to submit their paper to a journal (Scholze has a history of turning down large prizes…). It occurs to me that there are quite a few arithmetic geometers who understand well the problem with the proof, could write something up and possibly get it published. Maybe a collaboration could be formed to do this.

Update: New Scientist has a story here. The quotes from Fumiharu Kato aren’t especially encouraging for IUT, who “estimates that fewer than 10 people in the world comprehend the concept.”

Kato believes that the controversy stems from the fact that Mochizuki doesn’t want to promote his theory, talk to journalists or other mathematicians about it or present the idea in a more easily digestible format, believing his work speaks for itself. Kato says that his current and former students are also reticent to do the same because they see him “as a god” in mathematics and don’t want to go against his wishes.

Because of this, most mathematicians are “at a loss” for a way to understand IUT, says Kato, who concedes that, despite earlier optimism about the idea, it is possible that the theory will eventually be disproven.

Ivan Fesenko is much more of a believer:

He told New Scientist that there is no doubt about the correctness of IUT and that it all hinges on a deep understanding of an existing field called anabelian geometry.

“All negative public statements about the validity of IUT have been made by people who do not have proven expertise in anabelian geometry and who have zero research track record in anabelian geometry,” he says.

Update: Scientific American has a news story about this, which summarizes the situation with the proof as:

So despite Mochizuki’s latest publication, there is still doubt among experts about the state of the abc conjecture. Most number theorists cannot make up their own mind because they are unable to follow the proof. And because both Scholze and Mochizuki enjoy an excellent reputation in their field, it is unclear who is right.

This gets the story quite wrong, and misunderstands how mathematics works. The problem is that there is no proof that anyone (Mochizuki himself included) can explain to anyone else, this is not about “do I believe this guy or the other guy?”. Yes, most mathematicians don’t have the technical knowledge to evaluate this sort of proof, but there are plenty who do, and they are either saying there is no proof, or, for the few supporting the proof, unable to explain it to anyone else.

Posted in abc Conjecture | 40 Comments

The Work of Robert Langlands

This is more of an advertisement than a blog post. This evening on the arXiv James Arthur has posted a wonderful 204 page document explaining the work of Robert Langlands, written in conjunction with the award of the Abel Prize to Langlands.

This isn’t an introduction to the subject, but if you have some idea of what the Langlands program is about, it provides a wealth of valuable explanations at a more detailed level of exactly what Langlands discovered. It ends with a discussion of the “Beyond Endoscopy” program of his later career.

Posted in Langlands | 1 Comment