If I’m going to point to something about string theory and say the same things as always about it, seems best to first start with the opposite, an item about something really worth reading.

- This spring I’ve been teaching a graduate course aimed at getting to an explanation of the Standard Model aimed at mathematicians. The first few weeks have been about quantization and quantum mechanics, today I’m starting on quantum field theory, starting with developing the framework of non-relativistic QFT. While trying to figure out how best to pass from QM to QFT, I’ve kept coming across various aspects of this that I’ve always found confusing, never seen a good explanation of. Today I ran across a wonderful article by Thanu Padmanabhan, who I knew about just because of his very good introductory book on QFT, Quantum Field Theory: The why, what and how. The article is called “Obtaining the Non-relativistic Quantum Mechanics from Quantum Field Theory: Issues, Folklores and Facts” and subtitled “What happens to the anti-particles when you take the non-relativistic limit of QFT?” It contains a lot of very clear discussion of issues that come up when you try and think about the QM/QFT relationship, a sort of thing I haven’t seen anywhere else.
Looking for more of Padmanabhan’s writings, I was sad to find out that he passed away in 2021 at a relatively young age, which is a great loss. For more about him, there’s a collection of essays by those who knew him available here.

- For something I can’t recommend paying more attention to, New Scientist has an article labeled How to test String Theory, which is mostly an interview with Joseph Conlon. Conlon’s goal is to make the case for string theory, in its original form as a unified theory with compactified extra dimensions. On the issue of testability there’s nothing new, just the usual unfalsifiable story that among all of the extra stuff (moduli fields, axions, extra dimension, extended structures) that appears in string theory and that string theorists have to go to great trouble to make non-observable, it’s in principle conceivable that somebody might observe one of these things someday. But, that’s not really what people mean when they ask for a test. For details of the sort of thing he’s talking about in the New Scientist article, see here.
I strongly disagree with Conlon about some of what he’s saying, but the situation is very much like it has always been with many string theorists since way back to nearly forty years ago. We don’t disagree about the facts, it’s just that I’ve always looked at these facts and interpreted them as showing string theory unification ideas to be unpromising, whereas string theorists like Conlon somehow find reasons for optimism, or at least for believing there’s no better thing to do with their time. Last time I was in Oxford, Conlon invited me to lunch at his College and I enjoyed our conversation. I think we agreed on many topics, even about what is going on in string theory, but it looks like we’re always going to have diametrically opposed views on this particular question. For more from him, as far as popular books by string theorists go, his Why String Theory? book is about the best there is, see more about this here.

New Scientist this week has a cover story I can strongly endorse, entitled Why physicists are rethinking the route to a theory of everything. It’s by journalist Michael Brooks, partly based on a long conversation we had a month or so ago. Unfortunately it’s behind a paywall, but I’ll provide a summary and some extracts here.

For a more technical description of the ideas I’m pursuing that are discussed in the article, see this preprint, which was intended to be a very short and concise explanation of what I think is the most important new idea here. This semester I’m mainly working on teaching and writing up notes for an advanced course for math graduate students about the Standard Model. I’ll be adding to these as the semester goes on, but have just added preliminary versions of two chapters (9 and 10) about the geometry of vectors, spinors and twistors in four dimensions. These chapters give a careful explanation of the standard story, according to which spacetime vectors are a tensor product of left-handed and right-handed spinors. They don’t include a discussion of the alternative I’m pursuing: spacetime vectors are a tensor product of right-handed spinors and complex conjugated right-handed spinors. I’ll write more about that later, after the course is over end of April (and I’ve recovered with a vacation early May…).

It’s well-known to theorists that the Standard Model theory is largely determined by its choice of symmetries (spacetime and internal). A goal of these notes is to emphasize that aspect of the theory, rather than the usual point of view that this is all about writing down fields and the terms of a Lagrangian. This symmetry-based point of view should make it easier to see what happens when you make the sort of change in how the symmetries work that I’m proposing. What I’m not doing is looking for a new Lagrangian. All evidence is that we have the right Lagrangian (the Standard Model Lagrangian), but there is more to understand about its structure and how its symmetries work. In particular, the different choice of relation between vectors and spinors that I am proposing is not different if you just look at Minkowski spacetime, but is quite different if you look at Euclidean spacetime.

The New Scientist article has an overall theme of new ideas about unification grounded in geometry:

… a spate of new would-be final theories aren’t grounded in physics at all, but in a wild landscape of abstract geometry…

That might strike you as outlandish, but it makes sense to Peter Woit, a mathematician at Columbia University in New York. “Our best theories are already very deeply geometrical,” he says.

There’s some discussion of string theory and its problems, with David Berman’s characterization “It can be a theory of everything, but probably it’s a theory of too much.” The article goes on to describe the amplituhedron program, with quotes from Jaroslav Trnka. After noting that it only describes some specific theories, there’s

Trnka thinks the amplituhedron approach might enable us to go even further. “One can speculate that whatever the correct theory of everything is, it would be naturally described in the amplituhedron language,” he says.

Turning to a discussion of twistors, there’s then a section describing my ideas fairly well:

Woit is using spinors and twistors to create what he hopes are the foundations of a theory of everything. He describes space and time using vectors, which are mathematical instructions for how to move between two points in space and time – that are the product of two spinors. “The conventional thing to do has been to say that space-time vectors are products of a right-handed and a left-handed spinor,” says Woit. But he claims he has now worked out how to create space-time from two copies of the right-handed spinors.

The beauty of it, says Woit, is that this “right-handed space-time” leaves the left-handed spinors free to create particle physics. In quantum field theory, spinors are used to describe fermions, the particles of ordinary matter. So Woit’s insights into spinor geometry might lead to laws describing the holy trinity of space, time and matter.

The idea has got Woit excited. He has spent most of his career looking at other ideas, thinking they will go somewhere, and being disappointed. “But the more I looked at twistor theory, the more it didn’t fall apart,” he says. “Not only that, I keep discovering new ways in which it actually works.”

It isn’t that Woit believes he necessarily has the answers. But, he says, it is good to know that, despite the long search for a theory of everything, there are still new possibilities opening up. And a better, if not perfect, theory has to be out there, he reckons, one that at least deals with sticking points like dark matter. “If you look at what we have, and its problems, you know you can do better,” he says.

Other work that is described is Renate Loll and causal dynamical triangulations, as well as what Jesper Grimstrup and Johannes Aastrup call “quantum holonomy diffeomorphisms.” For more details of the Aastrup/Grimstrup ideas, see this preprint as well as Grimstrup’s website. I can also recommend his memoir, Shell Beach.

The article ends with:

]]>That said, when Woit – who has long been known as an arch cynic – is excited about the search for a theory of everything again, maybe all bets are off. Playing with twistors has changed him, he says. “I’ve spent most of my life saying that I don’t have a convincing idea and I don’t know anyone who does. But now I’m sending people emails saying: ‘Oh, I have this great idea’.”

Woit says it with a grin, acknowledging the hubris of thinking that maybe, after so many millennia, we might finally have cracked the universe open. “Of course, it may be that there’s something wrong with me,” he says. “Maybe I’ve just gotten old and just lost my way.”

This week at Harvard’s CMSA there’s a program on Arithmetic Quantum Field Theory that is starting up and will continue through March. There’s a series of introductory talks going on this week, by Minhyong Kim, Brian Williams, and David Ben-Zvi. I believe video and/or notes of the talks will be made available.

At the IHES, the Clausen-Scholze course on analytic stacks has just ended. For an article (in German) about them and the topic of the course, see here. What they’re working on provides some new very foundational ideas about spaces and geometry, in both the arithmetic and conventional real or complex geometry contexts. Many of the course lectures are pretty technical, but I recommend watching the last lecture, where Scholze explains what they hope can be done with these new foundations.

Of the applications, the one that interests me most is the one that was a motivation for Scholze to develop these ideas, the question of how to extend his work with Fargues on local Langlands as geometric Langlands to the case of real Lie groups. He’ll be giving a series of talks about this at the IAS next month.

Something to look forward to in the future is seeing the new Clausen-Scholze ideas about geometry and arithmetic showing up in the sort of relations between QFT, arithmetic and geometry being discussed at the CMSA.

]]>For the last thirty years or so, one tactic of those who refuse to admit the failure of string theory has been to go to the press with bogus claims of “we finally have found a way to get testable predictions from string theory!”. I’ve written about dozens and dozens of these over the years (see here). In recent years the number of these has tapered off considerably, as it likely has become harder and harder to find anyone who will take this seriously, given the track record of such claims.

Today Quanta magazine though has a new example, with an article that informs us

An idea derived from string theory suggests that dark matter is hiding in a (relatively) large extra dimension. The theory makes testable predictions that physicists are investigating now.

This is about a proposal for a micron-scale large extra dimension, with no significant connection to string theory. I took a look at the “predictions” (see here) long enough to assure myself it’s more of the same, better to not spend more of one’s time on it. One positive thing to say about the article is that the writer did go ask string theorist experts about this, and while these experts tried to be polite, they clearly weren’t enthusiastic:

While physicists find the dark dimension proposal intriguing, some are skeptical that it will work out. “Searching for extra dimensions through more precise experiments is a very interesting thing to do,” said Juan Maldacena, a physicist at the Institute for Advanced Study, “though I think that the probability of finding them is low.”

Joseph Conlon, a physicist at Oxford, shares that skepticism: “There are many ideas that would be important if true, but are probably not. This is one of them. The conjectures it is based on are somewhat ambitious, and I think the current evidence for them is rather weak.”

Better though would have been to ask Sabine Hossenfelder what she thinks about this kind of thing (or not write about them at all)…

]]>For a low-rent version of the self-congratulatory program discussed here, Bad Boy of Science Sam Gregson has a new video up entitled Particle Physics Is Not In Crisis – but we can make improvements. Cliff Burgess plays the Strominger role, explaining that the idea that there’s any problem with what’s going on in particle theory is “a nothing-burger” and “a complete non-issue”. Asked to rank any such problem on a scale of 0-10, he gives the Strominger-esque “.0001”. Martin Bauer goes for “1”.

The take on the question is much the same as Sean Carroll’s four-hour plus explanation that there is no problem, but shorter. It’s similar to Carroll in that no one who thinks there is a problem was invited to participate, or even gets mentioned by name. There’s a repeated reference to mysterious “Twitter influencers”, which I find very confusing because just about the only particle theorists I see spending time on Twitter going on about the state of the field are Bauer and Burgess. They can’t mean me since I’ve so far resisted the temptation to enter Twitter discussions. The idea of trying to have a serious discussion of complex scientific issues in the Twitter format never made any sense to me, and (StringKing aside) I find it hard to think of any tweets by anyone that shed any light on serious issues in this area.

The more serious part of the program was the discussion among the two HEP experimentalists of the state of their field, which got a 5-6 on the crisis level scale. I wrote about the problem there five years ago, and very little has changed, other than that we’re five years closer to the date when there will no longer be an energy frontier machine running anywhere in the world. The underlying problem wasn’t really explained. CERN is working on it, but there is as of now no specific plan with specific budget numbers for what to build next. Maybe I misunderstood, but it seemed that Bauer and others were talking about how the field just needed to convince funding agencies to support budget numbers of order \$100 billion, which is a pipe dream.

]]>A few quick links:

- There’s a one-day conference next Friday at the IHES, recognizing Dustin Clausen’s appointment to a new Jean-Pierre Bourguignon Chair. Should be several interesting talks, see here.
- There’s an ongoing conference at the KITP on the topic of What is String Theory? So far, none of the online talks address that issue. Evidently there was a discussion of the topic last Wednesday, but not recorded. Were any readers here in attendance and willing to report on that event? Next chance to find out what string theory is will be a Monday Blackboard Lunch talk by Gopakumar.
- In April there will be an IUT conference hosted by Zen University in Tokyo, see here. All the speakers but one are from RIMS. For news from the senior people devoted to IUT, Ivan Fesenko has moved to Westlake University in Hangzhou, and Shinichi Mochizuki is has been blogging here.
- There’s a new Shanghai Institute for Mathematics and Interdisciplinary Science, headed by Shing-Tung Yau.
- For those following what happens with the small number of permanent positions in particle theory, news from 4 gravitons.

For another podcast/interview with me that was recently recorded, see Maths, Twistors & String Theory. Know Time is a series of podcasts that is a project of Shalaj Lawania, and I was impressed by the effort he put into trying to make sense of a complicated and inaccessible subject. For an excellent pairing with what I have to say, see his earlier interview with Matthew Kleban, who has a more positive take on string theory, the multiverse, etc.

]]>Starting next week I’ll be teaching a graduate topics course, with the general plan to develop much of the quantum field theory of the Standard Model in a form accessible to mathematicians, emphasizing the connections to representation theory. There’s a course web-page here, notes will start appearing here once the course gets underway. While the course will be aimed at mathematicians, I’m hoping that some physicists might find it interesting and worth trying to follow.

The last time I did something like this was back in fall 2003. At that time the course was aimed at getting math students to the point of understanding the TQFTs for Chern-Simons theory and Donaldson theory and wasvvery much based on the path integral. This time I’ll be mostly sticking to flat space-time and using more representation theory. Also, a lot more about spinor geometry, as well about about how Euclidean and Minkowski space-time versions of QFT are related.

]]>I just finished watching the video here, which was released today. Since this was advertised as a panel discussion on the state of string theory, I thought earlier today that it might be a good opportunity to write something serious about about the state of string theory and its implications more generally for the state of hep-th. But, I just can’t do that now, since I found the video beyond depressing. I’ve seen a lot of string theory hype over the years, but on some level, this is by far the worst example I’ve ever seen. I started my career in awe of Edward Witten and David Gross, marveling at what they had done and were doing, honored to be able to learn wonderful things from them. Seeing their behavior in this video leaves me broken-hearted. What they have done over the past few decades and are doing now has laid waste to the subject I’ve been in love with since my teenage years. Maybe someday this field will recover from this, but I’m not getting any younger, so dubious that I’ll be around to see it.

Most shameful of the lot was Andy Strominger, who at one point graded string theory as “A+++”, another only “A+”. He did specify that very early on he had realized that actual string theory as an idea about unification was not going to work out. He now defines “string theory” as whatever he and others who used to do string theory are working on.

David Gross was the best of the lot, giving string theory a B+. At two points (29:30 and 40:13), after explaining the string theory unification vision of 1984-5 he started to say “Didn’t work out that way…” and “Unfortunately…”, but in each case Brian Greene started talking over him telling him to stop.

Funny thing is, I think even most string theorists are going to be appalled by this performance. Already, here’s what StringKing42069 has to say

]]>these old jagoffs have thrown an entire generation of strings under the bus. Fuq them.

I gave a “Spacetime is Right-handed” talk yesterday, part of a series entitled Octonions, standard model and unification. The slides are here, video should appear here.

Much of the talk was devoted to explaining the usual relation between spinors and vectors and how analytic continuation in complexified spacetime works then, from both the spinor and twistor point of view. This is contrasted to a new proposal for the relation between vectors and spinors in which the space-time degrees of freedom see only one of the two SL(2,C) factors of the usual complexified Lorentz group.

Nothing in the talk about using this for unification, where the idea is to exploit the other factor, which now appears as an internal symmetry. Starting from the point of view of Euclidean spacetime, the spacetime vectors and spinors that are related by Wick rotation to Minkowski spacetime degrees of freedom behave differently than usual, with a distinguished imaginary time direction. The general idea is that in standard Euclidean spacetime, where the geometry is governed by the rotation group SU(2) x SU(2), so splits into self-dual and anti-self-dual parts, one of these parts Wick rotates to spacetime symmetry, the other to an internal symmetry.

]]>There is a HEPAP meeting going on today, with release of the long-awaited P5 report prioritizing future HEP spending. The report is available here now, to be officially unveiled later in the day and discussed at the HEPAP meeting. The muon collider as a future project gets a strong endorsement as the “muon shot”.

More later

]]>Last month I recorded a podcast with Curt Jaimungal for his Theories of Everything site, and it’s now available with audio here, on Youtube here. There are quite a few other programs on the site well worth watching.

Much of the discussion in this program is about the general ideas I’m trying to pursue about spinors, twistors and unification. For more about the details of these, see arXiv preprints here and here, as well as blog entries here.

About the state of string theory, that’s a topic I find more and more disturbing, with little new though to say about it. It’s been dead now for a long time and most of the scientific community and the public at large are now aware of this. The ongoing publicity campaign from some of the most respected figures in theoretical physics to deny reality and claim that all is well with string theory is what is disturbing. Just in the last week or so, you can watch Cumrun Vafa and Brian Greene promoting string theory on Brian Keating’s channel, with Vafa explaining how string theory computes the mass of the electron. At the World Science Festival site there’s Juan Maldacena, with an upcoming program featuring Greene, Strominger, Vafa and Witten.

On Twitter, there’s now stringking42069, who is producing a torrent of well-informed cutting invective about what is going on in the string theory research community, supposedly from a true believer. It’s unclear whether this is a parody account trying to discredit string theory, or an extreme example of how far gone some string theorists now are.

To all those celebrating Thanksgiving tomorrow, may your travel problems be minimal and your get-togethers with friends and family a pleasure.

]]>I’ve just replaced the old version of my draft “spacetime is right-handed” paper (discussed here) with a new, hopefully improved version. If it is improved, thanks are due to a couple people who sent helpful comments on the older version, sometimes making clear that I wasn’t getting across at all the main idea. To further clarify what I’m claiming, here I’ll try and write out an informal explanation of what I see as the relevant fundamental issues about four-dimensional geometry, which appear even for $\mathbf R^4$, before one starts thinking about manifolds.

**Spinors, twistors and complex spacetime**

In complex spacetime $\mathbf C^4$ the story of spinors and twistors is quite simple and straightforward. Spinors are more fundamental than vectors: one can write the space $\mathbf C^4$ of vectors as the tensor product of two $\mathbf C^2$ spaces of spinors. Very special to four dimensions is that the (double cover of) the complex rotation group $Spin(4,\mathbf C)$ breaks up as the product

$$Spin(4,\mathbf C)=SL(2,\mathbf C)\times SL(2,\mathbf C)$$

where these two factors act on the spinor spaces.

While spinors are the irreducible objects for understanding complex four-dimensional rotations, twistors are the irreducible objects for understanding complex four-dimensional conformal transformations. Twistor space $T$ is a $\mathbf C^4$, with complex conformal transformations acting by the defining $SL(4,\mathbf C)$ action. A complex spacetime point is a $\mathbf C^2\subset T$ and conformally compactified complex spacetime is the Grassmannian of all such $\mathbf C^2\subset T=\mathbf C^4$. One of the spinor spaces at each point of complex spacetime is tautologically defined: it’s the point $\mathbf C^2$ itself (the other is of a different nature, with one definition the quotient space $T/\mathbf C^2$).

**Real forms**

While the twistor/spinor story for complex spacetime is quite simple, the story of real spacetime is much more complicated. When several different real spaces complexify to the same complex space, these are called “real forms” of the space. A real form can be characterized by a conjugation map $\sigma$ (an antilinear map on the complex space satisfying $\sigma^2=1$), with the real space the conjugation-invariant points. Using the obvious conjugation on $\mathbf C^4$, we get an easy to understand real form: the $\mathbf R^4$ with real coordinates, rotation group $SL(2,\mathbf R)\times SL(2,\mathbf R)$ and conformal group $SL(4,\mathbf R)$. Unfortunately, this real form seems to have nothing to do with physics, its invariant inner product is indefinite of signature $(2,2)$.

The real spacetime with Euclidean signature inner product has an unusual conjugation that is best understood using quaternions. If one picks an identification of the twistor space $T$ as $T=\mathbf C^4=\mathbf H^2$, then the conjugation is multiplication by the quaternion $\mathbf j$. The Euclidean conformal group is the group $SL(2,\mathbf H)$. The spinor spaces $\mathbf C^2$ are identified with two copies of the quaternions $\mathbf H$, with the rotation group now the group $Sp(1)\times Sp(1)$ of pairs of unit quaternions.

In this case the conjugation acts in a subtle manner. Since $\mathbf j^2$ is $-1$ rather than $1$, it’s not a conjugation on $T$, but is one on the projective space $PT=\mathbf CP^3$. It has no fixed points, so the twistor space has no real points. What is fixed are the quaternionic lines $\mathbf H\subset \mathbf H^2$, each of which corresponds to a point in the (conformally compacified, so $S^4=\mathbf HP^1$) real Euclidean signature spacetime. Using the decomposition as a tensor product of spinors, the action by $\mathbf j$ squares to $-1$ on each factor, but $1$ on the tensor product, where it gives a conjugation with fixed points the Euclidean spacetime.

The real spacetime with Minkowski signature is another real form of a subtle sort, with very different subtleties than in the Euclidean case. The conjugation $\sigma$ in this case doesn’t take the twistor space $T$ to itself, but takes $T$ to its dual space $T^*$. It takes spinors of one kind to spinors of the opposite kind (at the same time conjugating spinor coordinates to get anti-linearity). The Minkowski signature conformal group is the group $SU(2,2)$ and the rotation group is the Lorentz group $SL(2,\mathbf C)$ (acting diagonally on the two spinor spaces, with a conjugation on one side).

**Some philosophy**

The usual way in which the above real forms get used is that mathematicians ignore the Minkowski story and use the Euclidean signature real form to do four-dimensional Riemannian geometry, with the $Sp(1)\times Sp(1)$ decomposition at the Lie algebra level corresponding to the decomposition of two-forms into self-dual and anti-self-dual. Physicists on the other hand (especially Penrose and his school, but also those trying to do quantum gravity using Ashtekar variables) ignore the Euclidean story and use the Minkowski signature real form. In various places Penrose is quoted as explicitly skeptical of any relevance of the Euclidean story to physics. Working just with the Minkowski real form, one struggles with the fact that the Lorentz group is simple, but that one can get a very useful self/anti-self dual decomposition if one makes ones variables complex.

The point of view I’m taking is that Wick rotation tells one that one should look simultaneously at both Euclidean and Minkowski real forms, understanding how to get back and forth between them. This is standard in usual geometry where one just looks at vectors, but looking at spinors and twistors shows that something much more subtle is going on. The argument of this new paper is that when one does this, one finds that the spacetime degrees of freedom can be expressed purely in terms of one kind of spinor (right-handed by convention), the one that twistor theory tautologically associates to each point in spacetime. The other (left-handed) half of the spinor geometry involves a purely internal symmetry from the point of view of Minkowski spacetime. This should correspond to the electroweak gauge theory, exactly how that works is still under investigation…

]]>Dustin Clausen and Peter Scholze are giving a course together this fall on Analytic Stacks, with Clausen lecturing at the IHES, Scholze from Bonn. Here’s the syllabus:

The purpose of this course is to propose new foundations for analytic geometry. The topics covered are as follows:

1. Light condensed abelian groups.

2. Analytic rings.

3. Analytic stacks.

4. Examples.

Yesterday Clausen gave the first lecture (video here), explaining that the goal was to provide new foundations, encompassing several distinct possibilities currently in use (complex analytic spaces, locally analytic manifolds, rigid analytic geometry/adic spaces, Berkovich spaces). These new foundations in particular should work equally well for archimedean and non-archimedean geometry and hopefully will be the right language for bringing together the Fargues-Scholze geometrization of local Langlands at non-archimedean places with a new geometrization at the archimedean place. He describes as “(very) speculative” the possibility of a geometrization of global Langlands (with Scholze more optimistic about this than he is).

Tomorrow Scholze will take over, giving the next six lectures. Perhaps this characterization is a bit over-the-top, but seeing lectures of this sort and of this ambition taking place at the IHES brings to mind the glory days of Grothendieck’s years lecturing at the IHES on new foundations for algebraic geometry. I fear that keeping up on the details of this as it happens will require the energy of someone much younger than I am…

]]>I’ve finally managed to write up something short about an idea I’ve been working on for the last few months, so now have a preliminary draft version of a paper tentatively entitled Spacetime is Right-handed. One motivation for this is the problem of how to Wick rotate spinor fields, given that Minkowski and Euclidean spacetime spinors are quite different. In particular, it has always been a mystery why a Weyl spinor field has a simple description in Minkowski spacetime, but no such description in Euclidean spacetime, where the Euclidean version of Lorentz symmetry seems to require introducing fields of opposite chirality. The argument of this paper is that the relation between Euclidean and Minkowski is not the usual chirally-symmetric analytic continuation but something where both sides use just one chirality (“right-handed”). It’s quite remarkable that the dynamics of gauge fields and of GR also has a chiral-asymmetric formulation.

In the ideas about unification using QFT formulated in Euclidean twistor space that I’ve been working on the past few years, it was always unclear why, when you analytically continued back to Minkowski signature, the left-handed Euclidean spin symmetry would not go to the Lorentz boost symmetry, but to an internal symmetry. One goal of this paper is to answer that question.

This past weekend I recorded a podcast with Curt Jaimungal, which presumably will at some point appear on his Theories of Everything site. It includes some discussion of the ideas behind the new paper.

]]>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.

]]>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 thing 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 Clause on Analytic Stacks. Here at Columbia we have an ongoing seminar on some of the background for this, run by Juan Rodrigez-Camargo and John Morgan.

The math department at Columbia this fall will be hosting three special lecture series, each with some connection to physics:

- Sergiu Klainerman will be lecturing on the proof of nonlinear stability for slowly rotating black holes, Wednesday afternoons at 2:45.
- Nikita Nekrasov’s lectures will be on
*The Count of Instantons*, Friday afternoons at 1:30. - The Eilenberg lectures will be given by Laurent Fargues on Some new geometric structures in the Langlands program, Tuesdays at 4:10.

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.

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.

]]>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…

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