This semester the KITP has been running a program asking What is String Theory?, which is winding up next week, and was promising to “arrive at a deeper answer to the question in the title.” It seems though that this effort has gone nowhere, with this report from the scene:

Went to a string theory conference with many of the top researchers in the field centered around tackling the question “what is string theory” and the consensus after the conference was that nobody knows lmao

For an answer to the question from someone with a lot more experience, I recently noticed that Lubos Motl is very active on Quora, giving thousands of sensible answers to a range of questions, especially having to do with Central Europe. He explains the relation of string theory and M-theory (disagreeing with Wikipedia), and defines string theory as

the name of the consistent theory of quantum gravity which covers all the vacua found in the context of critical string theory and M-theory.

I had trouble getting my head around the concept of an undefined theory known to be consistent when I first heard about it nearly 30 years ago, but it seems to still be a thing.

Unrelated but I thought I would mention that Peter Higgs died earlier this week, 8th April

Dom,

I didn’t write a posting about this simply because I know nothing about him personally and nothing about his life’s work beyond having looked briefly at his two famous papers. Better that people get information about him and his life and discuss that at a better venue.

When I looked at the papers it was in the context of trying to carefully sort out the 1962-64 history, see

https://www.math.columbia.edu/~woit/wordpress/?p=3282

Lubos’s posts on quora are quite fascinating. Thank you for sharing that.

In the link https://www.math.columbia.edu/~woit/wordpress/?p=3282 in the Update at the bottom of the entry for “The Anderson-Higgs Mechanism”, the 1st “here” link goes to the American Journal of Physics website, but does not yield an expository article. Is something wrong with my browser, or is it the 1st “here” link?

One thing I’ve been very impressed with over the past twenty years is how Peter still doesn’t bear a grudge against those within the String community that were outrageously abusive towards him on their blogs. I used to have a blind admiration towards the intellectual talents of one String theorist in particular; but this was quickly eroded over the years by his bizarre views on identity politics in general and his belief in 2014 that the results of BICEP would be proven correct over those of the ‘jealous’ Planck collaboration.

Do you find the recent DESI results hinting at decaying dark energy instead of a cosmological constant to be any vindication of the string theory swampland problem, if the results hold up? Before I remember you posting that if de Sitter is in the swampland then the straightforward interpretation is string theory is wrong since the universe is asymptotically de Sitter. The new results suggest there could be gaps in this argument.

David Brown,

I’ve updated that link so that it works again (although the article is now behind a paywall).

Interested Amateur,

The string theory story makes clear that the smartest people in the world can be wrong about something and tenaciously hold fast to a wrong idea against all evidence. I’ve never held a grudge against Lubos (although on some days I have been rather angry that the senior people around him that he looked up to weren’t willing to explain to him that those who thought string theory was not the language in which God wrote the world had serious arguments and might be correct).

Anon,

The fact that no one knows what string theory is makes clear the nature of the “swampland program”. When people make a “swampland conjecture”, they are conjecturing behavior of an unknown theory. If experiment conflicts with this, you can’t use that to say the theory is wrong, since you don’t know what the theory is. All you can do is say that the experiment has told you something about the unknown theory. Vafa is quite explicit about this, that in his program new experimental evidence can never tell you that your fundamental theory is wrong, since you don’t know what it is. This isn’t a normal kind of science in which you have a notion of testing a theory that could be wrong. Here the “theory” is unknown, so can’t be wrong (so, one could say, “not even wrong”….).

@Peter Woit, a pdf for “A Question of Mass” by Jeremy Bernstein, 2010

can be found at a website at the Fluminense Federal University (Universidade Federal Fluminense) in Brazil:

http://profs.if.uff.br/tro/lib/exe/fetch.php?media=ajp000025.pdf

All,

Please, enough discussion of the Lubos Motl story, which is not the topic of this posting.

Peter,

>I had trouble getting my head around the concept of an undefined theory known to be consistent

But maybe the consistency is a part of definition, not a property of the theory! As in (to paraphrase Nathan Seiberg) “if we find a consistent theory of quantum gravity, we will call it String Theory”.

Peter, there is also a recent course on string theory at Perimeter institute (!)

Shantanu,

The Perimeter Institute long ago changed from its initial emphasis on research outside the dominant string theory-based ideology. The lectures on string theory this year by Gaiotto are likely much the same as ones he has been giving there since 2014. At this point the director of Perimeter is a string theorist, and they hosted the 2023 Strings conference. I guess one can argue that they are following their initial contrarian model, going all in on string theory during the years that most of the rest of the physics community has given up on it.

Having a graduate course on string theory is very common. I see two problems with these courses, and quickly looking at Gaiotto’s first lecture, his course likely will be an example:

1. The background and motivation given to the students is the same failed ideology that has killed the subject over the last 40 years. The students are not told any of the serious problems with this, why it doesn’t work.

2. The technical material is most of the time a detailed immersion in Polchinski’s string theory book. It may be the best string theory textbook, but it contains nothing about the problems with string theory, and it is a very challenging task for anyone to absorb the technical material it presents. The early graduate school years are crucial in training theorists, and if they spend one or more of these years immersed in the details of the quantization of the string, those are years in which they are not learning much more important things.

It could be worse though, Perimeter could be one of those institutions that teaches string theory at the undergraduate level….

But for sure there is also a course on loop gravity, noncommutative geometry, dynamical triangulation and all alternatives to string theory, right ?

Regge : QCD = string : quantum gravity

Peter,

I do my best to keep my course factual and hype-free. If you can pinpoint any inaccurate or deceptive statements, please let me know.

The main technical tools the students acquire during the course are the quantization of free fields in 2d, the definition of composite operators in free field theories and associated anomalies, some basic aspects of BRST quantization, the definition of disorder operators and boundary conditions in 2d free theories and rudiments of 2d CFT. Depending on the time availability, I may also sketch the ‘t Hooft expansion and the relation between bosonic and fermionic 2d QFTs (aka GSO projection).

Many of these tools are of general applicability in Theoretical Physics. I hope they will serve the students well independently of their final specialization.

Davide,

Thanks for your comment.

From what I understand you’re planning mostly a course on 2d qft, specifically CFT. That’s fine and some of the techniques are of more general use. My problem is really with the whole conception and framework of such a course.

If you were teaching condensed matter physicists and saying that the point of the whole thing was to study certain classes of condensed matter phenomena in 2d, that would be fine. But students are coming into this believing what Polchinski’s book and a 40 year old publicity campaign tell them, that the point of all this technology is a specific theory (the 10d critical superstring, defined by considering a CFT and doing very difficult integrations over moduli spaces of super Riemann surfaces). No one is telling them that the idea of doing this and getting QG + the SM by compactifying on a Calabi-Yau just doesn’t work.

Looking at your first lecture, you’re doing the standard thing of telling the students to think of a QFT as an integral over paths with complicated rules for how paths split and recombine. String theory is then motivated as going to an integral over surfaces.

But this isn’t what the standard model QFT is. It’s an integral over fields, with the fields having very specific and subtle geometrical significance (connections, spinors) and the action also having very specific and subtle geometrical significance (curvature, Dirac operator). The message the students get in most string theory courses is that the more advanced, deeper way of thinking about fundamental physics is to throw out all those structures and think about Riemann surfaces and 2d conformal symmetry.

In your first lecture you’re not talking about CFT or the QG/unification motivation, but about the “paths to surfaces” motivation and other motivations, leading up to drawing the usual M-theory conjectural diagram. Back in 1995 this was an interesting conjecture, but nearly 30 years later I think anyone trying to sell it to students needs to at the same time clearly explain that looking for such a new kind of fundamental theory has gone nowhere and essentially everyone has given up on it. I guess related to what you were trying to explain is the idea of relating string theory to a large N expansion of QCD, which would be a good motivation.

Maybe my fundamental problem these days is that calling a course “string theory” at a time when experts no longer mean anything in particular by the words “string theory” comes with the need to make clear to the students exactly what you mean by “string theory” and exactly what the motivation is for studying this specific thing. If you don’t do that, they’re going to think what you mean is the definition and motivation given in the textbook you assigned, which at this point have all sorts of serious problems no one is telling them about.

@ martibal, I’m currently visiting, I gave my small contribution to that balance you are mentioning 😉 It was however just an evening lecture to the master students on semiclassical spin networks, Regge geometries and spinors.

There used to be a course on loop quantum gravity (I taught it once myself but that was almost 20 year ago and for UW students, PSI didn’t even exist back then!), I dont know if it continues.

There is a LQG group here (of remarkably broad interests), a few students and postdocs working on LQG and on asymptotic safety, Renate Loll is a regular visitor for the CDT side, so fortunately `other games in town’ are still represented, and it is possible for the master students to get some exposure to them and broaden their perspectives.

Noncommutative geometry seems to have disappeared after having been well (but shortly) represented by M. Marcolli. A bit scary to see how a place which was highly advertised as its beginning as a paradise for original thinkers has been (at least partly) swallowed by string and AdS/ CFT (according to the master program visible on the website). It was not enough to be dominant in Princeton, ENS and other famous places, one had to be sure that no place dealing with high energy theoretical physics was spared from string,

2D CFT remains a very useful framework for nonperturbative calculations in condensed matter physics. The calculation by Cardy and Calabrese of entanglement entropy using twist operators is a masterful example, whereby one only uses the Schwarzian derivative to get the transformation of the stress tensor from a cut plane (representing the division into subsystems A and B) to the whole plane, and combine that with the conformal Ward identity for the 3-point function of the stress tensor and the two twist ops. It’s very hard to get the result even for free fields by elementary (constrained path integral) means–I’ve tried and failed!

Abelian and nonabelian bosonization remain useful for edge modes of topological liquids, spin chains, and 2D fractal surface-state wave functions of bulk topological superconductors. Also anyon statistics are ultimately traced back to monodromy properties of conformal blocks, although I get the impression that most workers in topological quantum computation bypass this.

On the other hand, though, the rate of new significant results is quite slow and there remains a steep learning curve to get through chapters 5-9 in the big yellow book, plus the prerequisite Lie algebra representation theory for WZNW models/nonabelian bosonization. Hence I don’t teach this stuff to grad students in a course, and I’m generally loathe to recommend it for self-study either–it’s just very hard to find good applications, for me at least. It’s a pity though because the material is some of the most “beautiful” in statistical physics.

@ Martibal

“Non-commutative Geometry” has not only been disappearing from the list of research areas represented in Perimeter … it has been almost completely disappearing from the panorama of research in fundamental physics and quantum gravity in particular. Practical first example: at the recent International Society for Quantum Gravity conference in Nijmegen Quantum Gravity 2023, where almost all areas of research in quantum gravity were significantly represented, there was not a single talk specifically dedicated to non-commutative geometry and the topic was barely mentioned in a few cases by researchers in other fields. Second example: in the recently published Handbook of Quantum Gravity there is not even a section properly dedicated to this subject. There might be many (and complex) reasons for such a “retreat” that are too long to be elaborated here.

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As someone ALSO currently teaching a graduate level course on string theory out of Polchinski’s book, I have to take exception. The original goal of string theory (getting quantum gravity in our world plus the standard model) has significant obstacles to overcome that no one currently knows how to tackle, this is fair enough. But still, at lesat in 10d superstrings give us a theory of quantum gravity in which graviton scattering order by order in perturbation theory is finite. That’s amazing. Nothing else like it is known to mankind. Future theorists should learn it as a proof of concept ast least. The fact that the tools and tricks one needs to understand on the way are useful beyond that is an added bonus. As graduate chair here at UT I am unfortunately responsible for cutting our string sequence down from 2 semesters to 1. I find it hard to justify why string theory should get more time than cosmology, particle physics or advanced GR (all of which we teach as 1 semester courses). But that one semester I’ll defned tooth and nail.

Andreas Karch,

We’ll just have to disagree about quantizing the 10d superstring and understanding the extremely complex story of how one is supposed to get amplitudes that have nothing to with the 4d world out of hopefully finite integrations over supermoduli spaces of super-Riemann surfaces.

On the list of things physicists have come up with that are amazing and worth teaching to students, I still think this topic is very, very far from the top.