# 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:

Zierler:

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?

Freedman:

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.

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### 23 Responses to The Philosophy of Supersymmetry

1. Molly says:

Your argument for spontaneous supersymmetry breaking being ugly and somehow a desperate attempt to make a theory agree with nature makes no sense. The generalisation of Abelian gauge theories to non-Abelian gauge theories could equally well be accused of being made ugly by desperate attempts to reconcile that with nature by shoving a mass into that theory either by hand or through the Higgs mechanism. You might say that’s different, we know it exists in nature, but that’s only a posteriori. The fact is both generalisations follow the same kind of logic and motivations. Note also that the first minimal attempts at the non-Abelian generalisations were also wrong. Had we happened to be technogically limited such that going up in energy took a decade per 10 GeV such that the W and Z were supposedly always around the corner but always disappointingly out of reach then no doubt non-Abelian theories would be the target of your polemic. Of course you’ll say something like “well that was different, we knew about neutral currents etc.” But it’s always easy to join up the dots in hindsight. My point is one that in principle non-Abelian and supersymmetric generalisations are very similar in philosophy and what experiment can tell us is something determined by the limitations of technology which nature doesn’t give a damn about. Yes it’s disappointing that supersymmetry is not where it could have been according to *one* specific argument. But had it taken say a century to go from 40 GeV to 80 GeV you’d have been there every step of the way berating non-Abelian theorists and their unscientific fanciful ideas led by group think. It’s ironic that you appear to be completely oblivious to your own twisted reasoning that’s no less delusional than Gordy Kane’s, only on the opposite anti-supersymmetry end of the spectrum. This anti-supersymmetry narrative is just as tiresome a broken record as the extreme pro-supersymmetry promises. The truth, as always, lies somewhere in the middle.

2. Peter Woit says:

“Molly”,
First of all, what’s with the fake name (I really doubt your name is Molly)? Could it be because you know very well that arguing that “in principle” the situation of the Weinberg-Salam model and the MSSM are “very similar in philosophy” is so silly that you don’t want your real name on it?

As you’re undoubtedly well aware, when Weinberg wrote his model down in 1967, the W and Z masses were determined by three parameters. The EM coupling + Fermi constant gave two out of three, so to nail down the W, Z masses you just needed to measure one more parameter (the Weinberg angle). According to you this is much the same thing as the early (and current…) situation of the MSSM, which I believe introduces about 105 new undetermined parameters.

So, you’re arguing that having one undetermined parameter and having 105 undetermined parameters is “very similar”? Whose reasoning here is “twisted” and “delusional”?

3. A long long time ago says:

Prefacing this by stating that weak-scale supersymmetry is mostly dead (but see Goldman, W (1973)), it’s not fair to say that people should have known better. Supersymmetry, like technicolor, is a very good idea that happens to be wrong. Supersymmetry gave a plausible way to make the Higgs mass natural, provides a dark matter candidate and makes the couplings unify more closely. Now it’s very easy to cavil at all these things, especially with the benefit of hindsight, and it’s clear that things didn’t work out. But the physicists excited by supersymmetry weren’t idiots and had very good reason to be excited. It’s the people who haven’t tempered their enthusiasm in response to the experimental evidence that are the problem.

4. Molly says:

I am not referring to the Weinberg-Salam model vs the MSSM, which are specific models in a more general framework. I am referring to the framework of non-Abelian gauge theories in general, going back to Yang and Mills, whose mathematical generalisation of the Lie algebra is very much in analogy with the further generalisation to a super Lie algebra. Pauli came up with this before but knew there no other massless gauge bosons that such a generalisation predicts. The Woit of the time would have derided attempts to rescue this theory by breaking the degenerate mass spectrum with an “ugly” spontaneous breaking mechanism. He would have pointed out that Glashow’s first minimal SU(2) attempt was already clearly excluded by experiment and scorned further model-building, such as adding an admixture of U(1), as just further desperate attempts to evade experiment rather than abandoning the fantasy. What next, SU(3)? SU(4)? SU(3)xSU(2)xU(1)? Gauge theories aren’t even predictive, he would say, you can always change your prediction by choosing a different SU(N)!

The point here is not about number of parameters; parameters parameterise ignorance, and ignorance is a technological limitation. If we happened to have experimental access to the susy-breaking mechanism then it would not be 105 parameters but ultimately a less arbitrary theory where supersymmetry relates parameters by symmetry in the same way we don’t consider 8 gluons to be uglier than a single photon because they’re related by SU(3). The difference in number of parameters and the extent to which one can determine them experimentally is a point of practicality.

It says something about physicist stereotypes that Molly is unfortunately not taken for granted as a real name for a physicist. In any case please consider that people may have legitimate reasons for preferring not to draw public attention to themselves. Just because you choose to publicise yourself with your arguments does not make anonymous arguments any less valid simply because you can’t make a mental profile of the person behind the arguments. Would it help to say I have never published a paper on supersymmetry? Could it be that I am not a lifelong SUSY fanatic but simply a student who took the time to learn the facts and formed my own reasoned opinion?

5. Peter Woit says:

A long long time ago,
Technicolor is an excellent example to contrast to supersymmetry. Like SUSY, it’s an initially very attractive idea (I was a grad student when it came out and well remember this appeal). But as you try and fit it with reality it gets more ugly (extended technicolor?), and as experimental evidence and theoretical work developed, most people lost interest, with a few hanging in there trying to make it work. This is normal science, and the question with SUSY is why didn’t it evolve in the same way, but instead took the turn to the pathological?

I’m very well aware that some of most enthusiastic SUSY advocates are people smarter, better-informed and much harder working than me. The phenomenon of their decades-long enthusiasm for what to me was an unpromising idea has always baffled me. The cases where this continues post LHC-results just strike me as inexplicably bizarre. One can have a reasonable argument about exactly when things turned pathological during the period 1974-present, but I don’t think one can reasonably argue that we’re not there now.

6. Peter Woit says:

“Molly”,
Ah, the “framework” nonsense. Can’t tell now whether I’m dealing with an earnest fool or a clever troll, strongly starting to suspect the latter. Enough.

7. I can still remember says:

The thing I want to do is to defend those physicists in the 80s. It was very reasonable for people to get excited about SUSY. It managed to solve multiple problems at once. And you call the MSSM an ugly theory, but it’s really not. It’s the phenomenological SUSY breaking lagrangian that’s a disaster. There was always hope that a compelling form of SUSY breaking might come along that could tame the mess.

And the difference with technicolor is that, as I understand it, the FCNC results made it pretty challenging relatively soon. For SUSY, it wasn’t until the Higgs mass started getting pretty high compared to the Z-mass that the experimental outlook started looking dimmer. As that happened and later with the lack of any sign of superpartners at the LHC and with the SUSY breaking mess not seeming to get much better, you saw more physicists getting pessimistic about weak scale SUSY.

I’m not going to defend the die-hards who still claim that SUSY must be the answer.

8. Alex says:

My take: let’s leave history for the historians of science. Who cares who was right in the 80s? It was a different context.

To me, the important thing is, what do we do today? The whole field of fundamental physics is in a languid state. Particle physics is in deep coma, quantum gravity is in fantasy land. People with authority are in denial that anything is wrong, science journalism is taken by hype. Young physicists are leaving, those who stay waste their talent in dead end fantasy theories. The whole situation is very dire to me.

9. Peter Woit says:

Alex,
I think one of the main reasons for the sorry state of the field is that no one wants to admit being wrong, no one wants to criticize respected figures in the field for continuing to push failed ideas, no one wants to look at what happened and find where things went wrong. So the field is dominated by a 50 year old failed conceptual framework (Planck scale superstrings/supergravity, GUTS, SUSY extensions of SM at some scale). As long as this conceptual framework is what people are trained in and live and work in, the hard job of finding an alternative is much harder.

10. DB says:

I’m mostly here to agree with “A long long time ago”. As a student in the 80’s, I learned that technicolor and supersymmetry were the two leading candidates to solve the hierarchy problem (weak scale far below Planck scale, avoid Higgs mass divergence), and technicolor was already on the way out. Plus the dark matter candidate (photino, or more generally neutralino), and the beauty of SUSY SU(5) (converging couplings, less proton decay), made it the most promising avenue of study.

11. Peter Woit says:

DB,
Yes, that’s the sales pitch that was being made for decades starting in the early 80s. The problem is that a few weak arguments for a complicated theory with no evidence don’t add up to a significant argument for such a theory. There always were some prominent people out there making every argument they could think of for SUSY, never breathing a word about the problems with the theory. Anyone mentioning these problems was a “contrarian” even though what they were saying about the problems with the theory was well known in the community.

If you look at occasions where theorists made bets on SUSY, significant majorities always were betting against, well aware of the problems even it they weren’t getting a lot of attention.

12. Peter Shor says:

It’s not just a 50-year-old failed conceptual framework that’s the problem.

The field seems to have this tendency to latch onto unproven ideas long before they’ve demonstrated their ability to stand up. Look at Susskind’s idea of black hole complementarity from 1993, which didn’t have very much evidence for it, but was accepted by many researchers for nearly 20 years, until it succumbed to the AMPS paper in 2012.

I’m not at all convinced the same thing isn’t going to happen to the latest craze, non-isometric quantum codes; these seem to violate so many principles of quantum information that I don’t see how they can possibly work.

This wouldn’t be a problem, if researchers in the field didn’t have the tendency to dismiss alternative ideas with the reasoning “we’ve already solved that.”

13. Anonymous says:

“My belief in a credible and interesting physical theory isn’t going to hurt anybody.”

Except perhaps for the younger researchers who are forced to work on theories they do not believe in to please the boss.

14. Peter Woit says:

One thing that I realized is strange about about this history is that somehow skeptics of SUSY got labeled as “contrarians”, with SUSY “mainstream science”, which is completely backwards. From my conversations with theorists over many years, at no time were SUSY models ever something that most people found convincing. For evidence of this, see for instance here
https://strings.ph.qmul.ac.uk/~dsb/dbwager.pdf

Given the negative LHC results, at this point I’d argue that anyone still promoting SUSY extensions to the SM is somewhere on the spectrum from “contrarian” to “crackpot”, with the likes of Sabine Hossenfelder holding down the centrist, mainstream position.

15. Amitabh Lath says:

So I’m guessing nobody here feels that the 5.1 sigma discrepancy with theory reported by the Fermilab g-2 experiment is due to SUSY or her siblings?

16. Kurt Schmidt says:

The muon g-2 discrepancy is a 5.1 sigma discrepancy between two different ways of calculating the dipole moment from the Standard Model, one of which already agrees with the experiment. There is no need for beyond Standard Model physics, much more likely is the case that the other method is flawed and needs correcting.

17. Peter Woit says:

Amit,
At this point the SM being wrong by 5.1 sigma is an extraordinary claim, and given the theoretical complexities, the evidence is far from extraordinary. Seems likely one of the theory calculations is just wrong (or uses data wrong).

If the SM is wrong, personally I doubt what we’re seeing is SUSY, should be something much more interesting….

18. Amitabh Lath says:

Kurt, should we be giving more weight to the theory that agrees with experiment (the BMW calculation) or the other one that shows the huge tension (if they have a clever acronym I missed it)? The latter seems to be a bigger collaboration so I have been hedging that way.
In any case, the big theory issue is lack of e+e- –> hadrons data, which is being addressed. The g-2 experiment is still not systematics limited and has a lot more data to analyze. So both theory and experimental uncertainties will shrink in the next 2 years of so. As Peter says, probably not SUSY but interesting…

19. Hiro Kawabata says:

It seems that the theorists have considerable work to do on their calculations, including discrepancies in the data used for the dispersive method and the discrepancy between the dispersive and lattice QCD methods, before any claims of BSM physics can be made:

https://muon-gm2-theory.illinois.edu

20. Peter Woit says:

Maybe that’s enough about muon g-2, where the issues have nothing to do with SUSY.

A generic problem with the idea of using precision measurements like g-2 to get information about BSM physics is that if your BSM models (like MSSM) have loads of extra particles and parameters, a measured g-2 anomaly due to MSSM effects is going to give you one number, which is a very complicated function of the the many parameters you’d like to know about. In any case, right now we don’t even have that.

Dear Peter,
you should exercise some prudence when discussing Daniel Freedman.

Freedman is a very good mathematical physicist. He never over claimed
his results. He has a long trajectory of serious, correct and hard work. You are criticising him for what is an opinion (or a belief). He states this very clearly. He never forced anyone to work on his topics. Young researchers approached him in the last 50+ years (to work with him). Daniel Freedman is an example of serious, hard, concentrated work. Sticking to correct and elaborated calculations.

Again, you should be less critic of serious people, in particular if they state their beliefs and opinions, making clearly their character!

22. Peter Woit says:

Note that what I was doing was not criticizing Freedman or his work, but pointing to a long interview with him that people could read for themselves. I found his defense of continuing to work on a failed research program revealing.

As for not criticizing serious people, sorry, but when their ideas are wrong they (the ideas) should be criticized, and I’m not going to apologize for doing so.

23. kitchin says:

Again I’ll recommend also the Frenkel interview by Brian Keating, because it’s shorter. https://www.youtube.com/watch?v=b67o24J3bAs

At 27:00 Keating asks him about string landscapes and multiverses, but turns the question to whether there could be different maths in these universes, perhaps even without proof by contrapositive (“modus tollens”), or at least a different value of pi. So what is Frenkel to do with such a question? He starts talking about an alien species without numbers, such as the unitary intelligence in the movie Solaris, that would discover our same math by homotopy theory! He illustrates homotopy classes by imagining winding dental floss around your finger. Now that’s a string.

Strings are otherwise not mentioned in the interview as I recall it.

While it’s a popular math book, I would have liked to have had Frenkel’s Love and Math in grad school, to get an overview of the specialties I was studying. It’s a good book for many reasons, and can be usefully skimmed in about the same amount of time as the longer videos, or maybe twice that time.