The “SUSY Bet” event in Copenhagen took place today, with video available for a while at this site. It appears to be gone for the moment, will put up a better link if it becomes available. An expensive bottle of cognac was presented by Nima Arkani-Hamed to Poul Damgaard, conceding loss of the bet. On the larger question of the significance of the negative LHC results, a recorded statement by Gerard ‘t Hooft (who had bet against SUSY), and a statement by Stephen Hawking (not in on the bet, but in the audience) claimed that if arguments for SUSY were correct, the LHC should have seen something, so they think nature has spoken and there’s something wrong with the idea.

The losers of the bet who spoke, (Arkani-Hamed, David Gross and David Shih) demonstrated the lesson about science that supersymmetry and superstring theory have taught us: particle theorists backing these ideas won’t give up on them, no matter what. They all took the position that they still weren’t giving up on SUSY, despite losing the bet. In more detail:

- Arkani-Hamed was not a signatory of the original bet in 2000, but signed on to the later 2011 version. He explained today that at the time he thought chances of SUSY visible early on at the LHC were just 50/50 (with his 2004 work on split SUSY motivated by realizing that pre-LHC the conventional picture of SUSY at the electroweak scale was already ruled out). He attributed his decision to take the pro-SUSY side of a 50/50 bet to “optimism”, implying that this took place at a conference dinner where there may have been too much to drink. In his split-SUSY scenario, SUSY may yet show up at the LHC, or it could even be invisible there, requiring a higher energy accelerator. So, he’s not giving up on SUSY based on LHC results.
- David Gross also is not giving up, arguing that fine tuning of a factor of 100 or 1000 is not a problem (invoking the large ratios that appear in the fundamental Yukawa couplings). He did say that young people might want to take this as reason to look for new ideas, but, for himself, felt “I’m too old for that”.
- David Shih isn’t giving up either, arguing that there still was lots of data to come, plenty of room for SUSY to appear at the LHC, still believes we’ll discover SUSY, at the LHC or elsewhere.

One piece of misinformation promoted by several of the speakers was the idea that “everyone” back around 2000 believed in SUSY as the next new physics to be found. In my book (written in 2002-3) I wrote a long section about the evidence against SUSY, and, of course, if you look at the bet under discussion, in 2000 many more people (16 vs. 7) were taking the anti-SUSY vs. pro-SUSY side (at least in Copenhagen, but I think this reflects the general range of opinions).

No one today asked the obvious question “Is there any forseeable experimental data that would cause you to decide that SUSY was an idea that should be abandoned?”. I’m now not seeing any prospect in my lifetime of anything that would cause these or other SUSY proponents to give up (John Ellis has also announced that no matter what the LHC says, he’s not giving up). Unfortunately “Not Ever Wrong” is clearly the slogan of the (minority) segment of the particle theory community that long ago signed up for the vision of fundamental physics in which SUSY plays a critical part.

**Update**: There’s a blog entry from Natalie Wolchover about this. She has more detail about the final remarks from Gross that I mentioned:

“In the absence of any positive experimental evidence for supersymmetry,” Gross said, “it’s a good time to scare the hell out of the young people in the audience and tell them: ‘Don’t follow your elders. … Go out and look for something new and crazy and powerful and different. Different, especially.’ That’s definitely a good lesson. But I’m too old for that.”

**Update**: Video of the Copenhagen event is available here.

**Update**: I happened to be looking at Michael Dine’s 2007 Physics Today article on string theory and the LHC, noticed the side remark that “The Large Hadron Collider will either make a spectacular discovery or rule out supersymmetry entirely.” I wonder if he still thinks this, and whether we’ll ever see Physics Today publishing something updating its readers.

**Update**: Yet another news story about this, from Science News.

Peter,

I completely agree with you re. the “ugliness” of super symmetry as a solution to a hypothetical “naturalness problem”, and that we should not just have faith that it will ultimately somehow turn out to be correct after all (despite needing fine tuning to reduce fine tuning). [One should note, however, that “ugliness”, just like “beauty”, is not a valid criterion for deciding the correctness of a theory. :)]

I was just giving Gross the benefit of the doubt in his statement that we don’t understand the parameters of super symmetry buried in the couplings with the Higgs, yet, just like we don’t have a clue about other open issues with the SM itself. And we need to.

My interpretation is that he hopes/wishes/fantasizes [take your pick] that, once we understand what is really going on, those 100+ parameters will not just be explained, but will most likely disappear. His analogy was that, just like the morass of hadrons and their constituents was clarified once we understood gauge theory and asymptotic freedom in QCD, a more basic understanding of the underlying dynamics of Higgs interactions is what is required to clear up what is really going on in the morass that is super symmetry and the naturalness “problem” — and perhaps other SM issues as well. And that will require understanding those Higgs couplings much better.

Of course, a fundamental difference is that the issues in the 1960s with hadrons and quark confinement were the results of multiple experiments. The issues thrown up by super symmetry are strictly theoretical, solving a theoretical problem, with essentially no experimental guidance or even confirmation of the problems themselves, other than negative ones. But my interpretation of his current approach is to say, OK, we don’t know what’s going on, but let’s start by assuming some kind of super symmetry effectively exists and see if that can lead us to the deeper understanding where we can explain it away.

That’s obviously just my interpretation from several of Gross’s talks. It’s very different from just “believing in SUSY” (like some of those panelists apparently still do). And it could be considered increasingly foolhardy as decades of experiments accumulate against that hope. It would be interesting to hear his actual thoughts spelled out.

I had a stint with theoretical particle physics a long time back, I did some supersymmetrical calculations, then switched to experimental particle physics. To my understanding, the best argument for SUSY was that if supersymmetry were realized in nature, there would be a Nobel for my university (well, until Julius Wess’s untimely passing). The second best argument was the pure ingenuity of QFT that forces you to discover supersymmetry if you are creative and study its mathematics hard enough. I always felt that these arguments were more convincing than “it gives you dark matter (once you assume an additional symmetry)” and “it cures a mathematical-aesthetical problem that you have when you extrapolate to arbitrarily large energies assuming that there are no unknowns on the way there.” This skeptical point of view may have been reinforced by my very pragmatic advisor, who never bought the hype, and who is still at the forefront of pure standard model calculation, but who at the time wanted to do a few SUSY calculations in order to learn the formalism himself. (BTW I would like to remind everyone that recent progress in SM calculations has been tremendous, so it’s not at all like theoretical particle physics is not making progress, and the progress is actually very much related to better understanding of the mathematical structures even though generalized polylogarithms and numerical-analytical methods probably aren’t as sexy as amplituhedra.)

Anyway, what I originally wanted to point out is that talking about hundreds of parameters as a deficit of SUSY is not attacking one of its weak points. The idea, as I understood it then, was that we need all these parameters because we don’t understand how supersymmetry is broken, so they parameterize our ignorance and if we keep them, we avoid prejudice about the unknown: if you assume that SUSY is a fundamental symmetry, you also assume that, say, the mass of the electron and the selectron are related by the same mechanism that relates the mass of the muon and the smuon. Thus nobody who believes in SUSY believes that the masses of selectron and smuon are independent parameters (provided of course that the SM parameters are known inputs). The large number of parameters is a convenience, and allows very general experimental exploration, exactly because it doesn’t require to specifiy the mechanism of SUSY breaking.

This seems to imply that someone should keep track of which models of SUSY breaking have been excluded, but I don’t think I’ve seen anything like that. Maybe even with SUSY breaking there’s more freedom left than I could possibly imagine?

TS,

It’s true that the huge number of new parameters problem is not fundamental, in the sense that one can always claim that “all that is needed is to figure out the mechanism of supersymmetry breaking”. On the other hand, despite 40 years of effort, no one has come up with any compelling such mechanism (i.e. one that explains something about known physics, or does anything other than multiplying entities and adding complexity on a scale larger than the number of phenomena one is trying to explain). The extra parameters issue is a quick way of referring to that problem, since examining in detail all the possible mechanisms for susy breaking and their problems leads to absurd complexity (such that this is an issue that theorists appear to have pretty much abandoned, as far as I can tell, few people still work on it). And, these mechanisms completely torpedo claims to have a “beautiful” or “elegant” theory.

Seems like ‘t Hooft and Peter W should have placed side-bets on the “We lost, but we could still win” reaction from the usual SUSYpects.

The debacle also seems to leave Popper’s idea of refutation looking pretty underpowered when it comes to theories like SUSY, with so many tunable parameters.

Maybe this week we’ve seen the emergence of a new criterion for such theories: “aleatory refutation” – aka Death by Wager.

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” John Ellis has also announced that no matter what the LHC says, he’s not giving up ”A man has declared his mind closed. I have respect for self-knowledge.

There were always many arguments against low energy supersymmetry, both empirical and aesthetic. The searches for superpartners at the LHC coming up empty is only the latest, strongest empirical argument against low energy supersymmetry. The aesthetic is as soon as one took the beautiful idea of supersymmetry and tried to match it to nature, it rapidly became ugly. It is a solution in search of a problem, like a cave man finding by chance a shiny MacPowerBook and after puzzling over what to do with it, uses it as a hammer.

That doesn’t mean that supersymmetry has no place in physics, any more than that the laptop has no use good use. Solid mathematics has a way of finding a realization in physics. It’s that aesthetic appeal of supersymmetry that leads to its advocates not giving up on it. It’s just that we haven’t yet found that proper place, and in the meantime we should probably give up viewing it as a hammer.

More seriously, the most compelling argument against low energy supersymmetry was always that although it was advocated on the basis of ‘naturalness’ to cancel quadratic cutoff dependence and explain the light Higgs vs. the Planck mass, it provided and still provides no answer to the biggest naturalness problem of all–namely the smallness of the vacuum energy in Planck units. By itself this is telling us with certainty that supersymmetry cannot solve all naturalness problems associated with the Planck scale, which will require a much better understanding of how quantum theory and Einstein’s gravity fit together.

Uses of supersymmetry – am under the impression that the BRST formalism relies on supersymmetry? So, mathematically, not physically, supersymmetry is realized in every non-abelian gauge theory?

Anonyrat,

It depends what you mean by “supersymmetry”. If you mean generically use of a Lie superalgebra, then BRST is an example. But usually “supersymmetry” in this context means a specific Lie superalgebra, a non-trivial extension of the Poincare group. BRST treatment of gauge symmetry doesn’t involve space-time symmetries.

I agree with Emil that probably what’s going on here is that “supersymmetry” has some different role in fundamental physics. I’d guess that you want to use Lie superalgebras in the context of space-time symmetries, but the particular extension of the Poincare group and the representations of this that people have been trying to connect to reality don’t work (and I think the problem is not just a low energy one). Perhaps you want something more like the way superalgebras appear in BRST.

Anonyrat, BRST and SUSY are very different.

In BRST y0u have a single Grassmann-odd operator that squares to zero and is used to conveniently encode and impose the gauge constraints on the state space. The constraints can generally be imposed in other ways that are more complicated in practice but don’t require the BRST formalism. BRST doesn’t add any physical states that are not in the original gauge theory. The whole point of BRST is that the “ghosts” we introduce should factor out of the state space and in addition cancel out gauge-redundant degrees of freedom. So BRST reduces the state space as opposed to increasing it.

In SUSY you have a set of Grassmann-odd operators that, when “squared,” give spacetime translations (not zero as in BRST). SUSY can thus be seen as an extension of spacetime, adding Grassmann-odd “directions” besides the usual 3+1. Field vibration modes in the new odd directions provide superpartners to the usual particles in ordinary spacetime. So, in contrast to BRST, adding SUSY to a model provides extra physical states.

NoGo: I think the main attraction of SUSY is that it offered a way around certain problems in the construction of a consistent unified field theory of all four interactions. Plus, as the last possible symmetry of the Poincare group, it would seem a pity that Nature might not avail of it!

Re the zeitgeist, it seems to me that many commentators such as Johnnythelowery have things the wrong way around; the current zeitgeist is SUSY skepticism, not SUSY optimism (at least if judged by blogs, media articles and pop science). Which is strange because only low-energy SUSY has been ruled out so far.

Indeed, it seems to me that most commentators have misunderstood the nature of the bet – it was whether SUSY particles would show up by a certain energy range. A silly bet to be sure, but to interpret the negative result as ‘SUSY dead’ rather than ‘SUSY looking less likely’ is simplistic..

anon,

That’s a good explanation of the usual point of view. I find it interesting though that there are contexts where these things are not so different, with one of them Witten’s N=2 (twisted) SUSY YM theory that gives Donaldson invariants. In that case, among the supercharges is one that can be interpreted as a BRST differential

Much more generally, the interesting mathematical applications of SUSY theories often just look at “BPS states”, using a construction closer to the BRST one. It may be that the right perspective on SUSY theories is that most of the states are more like “ghosts”, not physical. And at the same time, I’m suspicious that BRST is more fundamental than people think, really needed to properly understand what is going on with gauge symmetry.

Hi, Cormac,

I think many of us outsiders understand (to the extent our brains allow) that there many ways to look at SUSY and what it might do. As an outsider, I’ve been surprised at the relative lack of discussion in the popular literature about the unique ability of SUSY to combine space-time and internal symmetries. I’d love to see more popular exposition about that aspect of the theory and why it is or isn’t compelling on its own. Then again, the relevant energy for that idea (in isolation) appears to be around the Planck scale, so maybe that’s why it’s not so interesting.

The other idea, the one where the superpartners that come with this unification have anything to do with the Higgs mass or a viable dark matter candidate? That idea seems to be bad shape, given the empirical evidence. It’s not clear to me what optimism or pessimism has to do with it anymore. Experiment has told us that if SUSY is relevant to these aspects of nature, it’s reportedly “very cleverly hidden”. That seems to be a nice way of saying it’s no longer plausible, if it ever was.

LMMI,

SUSY doesn’t really combine space-time and internal symmetries, it’s an extension of the space-time symmetries, commutes with the internal ones.

Hi, Peter,

Yes, thanks for correcting my imprecise description. I’m pretty much directly quoting another source directly, which delves into just what you said in detail that rapidly starts flying over my head (I’m not at all qualified to even get into the Coleman-Mandula no-go theorem and the nitty-gritty of why SUSY is the one-and-only non-trivial way to circumvent it, except to say I recognize this is important and interesting in its own right).

I would like to comment that there is a supersymmetry other than SUSY or BRS, but yet consistent with the unitarity of the physical S-matrix. I believe that it is natural to supersymmetrize only the local Lorentz symmetry of the Einstein gravity, because it commutes with the spacetime symmetry. The Lorentz symmetry SO(3,1) is extended to the orthosymplectic superalgebra OSp(N, 2; C). In this extension, {Q, Q} and {Q^(bar), Q^(bar}} are identified with M_(mu, nu), but {Q, Q^(bar)}=0.

From a mathematician’s viewpoint, spacetime supersymmetry is just one aspect of “supermathematics”, namely the replacement of vector spaces, manifolds, Lie groups, Lie algebras, commutative algebras and so on by their Z/2-graded versions. This is a remarkably potent idea – for example, it provides new improved proofs of the Atiyah-Singer index theorem, the positive mass theorem in general relativity, and a new outlook on differential forms.

Moreover, supermathematics is not an

arbitrarygeneralization of ordinary mathematics: there are plenty of theorems explaining how this Z/2-graded generalization is uniquely singled out. For an example, I recommend Urs Schreiber’s post on Deligne’s theorem, but can’t resist mentioning the closely related result that I proved earlier.I’m sure all this is somewhere in the back of the minds of physicists who think supersymmetry is “the only game in town”: there are few other principles with such wide-ranging connections to beautiful mathematics – except of course for those that have already been widely adopted in physics, such as gauge invariance, diffeomorphism-invariance, or the principle of least action.

The problem, of course, is that spacetime symmetry focuses our attention on a collection of staggeringly beautiful physical theories – such as 10-dimensional superstring theory and 11-dimensional supergravity – which seem to describe worlds

utterly unlike our universe. And when people try to tweak these theories to make them physically realistic, they – so far – become ugly and complicated.So, back when I was interested in figuring out the fundamental laws of nature, I avoided having anything to do with supersymmetry. Only after I quit that and took up pure math for a while did I come to appreciate its beauty! I especially enjoy how superstrings and supergravity are connected to n-categories and normed division algebras, with the octonions being closely connected to 10- and 11-dimensional spacetime supersymmetry.

I think it’s possible to take a balanced attitude and enjoy the beautiful mathematics of supersymmetry while taking an agnostic or even jaundiced attitude to whether it’s relevant to particle physics. But this is, of course, nearly impossible for people who hae staked their careers on it.

John Baez,

when you say that supersymmetry is a remarkably potent idea that provides for example a new improved proof of the positive mass theorem in general relativity, are you just referring to Witten’s 1981 article “A new proof of the positive energy theorem”? Its fourth section starts as follows: “In this section a few speculative remarks will be made about the not altogether clear relation between the previous argument and supergravity.” Has this become clearer later?

Independently of the answer (which I’m really interested in), my point is this. There are many examples in differential geometry where spinors are important to solve problems whose statements do not already involve spinors. The positive mass theorem is certainly such an example. But is it an example for the usefulness of supersymmetry? Would a Z_2 grading on geometric objects make the spinorial proof easier or more elegant in any way? Knowing the analytic details of the proof quite well, I doubt that. So, while I agree with you that one should “enjoy the beautiful mathematics of supersymmetry”, I think there is a danger of overhyping supersymmetry as a panacea already in pure mathematics.

I see an analogy to the discussion of physics we are having here. Obviously fermions (i.e., spinors) are needed to describe the universe we live in. But do we need supersymmetry to describe the universe? Even if we ignore (absence of) experimental evidence, would a Z_2 grading that puts bosons and fermions on the same footing really make our description of fundamental physics easier or more elegant? Everyone has to judge for themselves, but I doubt this one, too. From a purely geometric and representation-theoretic viewpoint, I find the Standard Model quite elegant the way it is; and the few aspects that lack elegance would not be remedied by supersymmetry.

Marc Nardmann/John Baez,

Once you expand the term “supersymmetry” to include all uses of Z2-graded mathematical structures, it doesn’t make sense to argue about whether it is related to physics. Of course it is, very fundamentally (the Dirac operator is the supercharge of a supersymmetric QM theory). The problem though is “which Z2-graded mathematical structure”? There a huge universe of them, as big or bigger than the universe of all more conventional mathematical structures. It becomes impossible to say anything true but non-trivial about such a universe.

A more useful discussion is to distinguish between what parts of this general Z2-graded universe reflect something deep about physics and/or mathematics (certain SUSY QM models) and what parts don’t seem to (SUSY extensions of the SM)

Peter Woit,

you said: “A more useful discussion is to distinguish between what parts of this general Z2-graded universe reflect something deep about physics and/or mathematics […]” That is closely related to the point I wanted to make: I agree that there are many places in differential geometry where spinors and Dirac operators can be used in “deep” ways, in contexts that do not a priori involve spinors. Does this already justify — probably by definition — to say that “supersymmetry” is used there in a nontrivial way? If so, then I will not argue with that definition. If not, then I argue that the positive mass theorem is not a good example of a deep application of supersymmetry. This is roughly analogous to the fact that we would not call the plain Standard Model (which involves spinors and Dirac operators) a “supersymmetric” theory.

Marc Nardmann wrote:

> When you say that supersymmetry is a remarkably potent idea that provides for example a new improved proof of the positive mass theorem in general relativity…

It’s late at night here in Singapore, so I’ll try to answer your questions later, but for now let me just note that I didn’t say that. I tried to be quite careful in how I expressed myself, saying:

> From a mathematician’s viewpoint, spacetime supersymmetry is just one aspect of “supermathematics”, namely the replacement of vector spaces, manifolds, Lie groups, Lie algebras, commutative algebras and so on by their Z/2-graded versions. This is a remarkably potent idea…

Maybe it wasn’t clear, but “this” refers to “supermathematics”, not supersymmetry.

John Baez wrote: “Maybe it wasn’t clear, but ‘this’ refers to ‘supermathematics’, not supersymmetry.”

That was indeed not clear to me. I apologise for mis-paraphrasing. So, which Z_2-graded objects were you alluding to in the context of the positive mass theorem?

You mentioned the application of “super” concepts in proofs of (versions of) the Atiyah-Singer index theorem. This seems to me to be a good example of the potency of “super” ideas. I still do not see how the positive mass theorem is an example. To me, it is just an example of the usefulness of spinors in differential geometry — which is profound, but not “super” in a technical sense.

The fact that the worline theory of an ordinary spinning particle (such as the electron) is 1d supersymmetric (see here for details and references) is interesting mostly because it is a precursor of the fact that the worldsheet theory of the “spinning string” (as it was originally called) just so happens to be 2d supersymmetric (and called the “superstring” only once this was realized), which in turn is interesting because it miraculously implies that the effective spacetime theory of which these strings are quata is locally 10d supersymmetric. This is interesting because, while the automatic worldline supersymmetry of the electron does not imply that the spacetime theory is supersymmetric, just assuming that the electron is the point particle limit of a string (and nothing else) does imply local spacetime supersymmetry. This is a key prediction of the assumption of strings:

strings & fermioms => supergravity

This of course does not prove that local spacetime supersymmetry (supergravity) is realistic, but it is one of the theorems that miraculously imply local spacetime supersymmetry and thus make it a plausible possibility. Of course this particular argument does require the assumption that particles are limits of strings, which might be wrong, and if so then the conclusion wouldn’t follow, of course.

On the other hand Deligne’s theorem needs no assumption beyond established principles of quantum physics (that elementary particles are labled by irreducible linear representations of the local spacetime symmetry group), but as a payoff it does not imply that the local spacetime symmetry group is the super-Poincare group, it only implies that among all imaginable modifications of local spacetime supersymmetry (e.g. non-commutative groups, aka quantum groups or more bizarre possbilitities) all except precisely the class of super-symmetry groups are excluded on mathematical grounds.

Combined with the observavation made in 1922, that the world does contain fermions, and the realization, a little later, that hence the phase space of every realistic physical theory (such as the standard model) is a supermanifold (the fermions constituting the odd-graded coordinates) it makes it rather plausible that the local symmetry group acting on this supermanifold in general mixed bosons and fermions, hence be a supersymmetry group. Of course this is not logically implied and could well be wrong, but the point to notice is that given the above circumstances, it would almost seem to require _more_ explanation why it shouldn’t, than the other way around: experiment shows that phase space is a supermanifold, and Deligne’s theorem says that the most general local spacetime symmetry group may be a supergroup, so why on earth would Nature then choose to constrain this possibility and have an ordinary group act on the supermanifold, if it could choose a supergroup.

Again, this does of course not prove local spacetime supersymmetry, but it serves to show that there are good reasons to expect that it might be: Because conversely, if the world were not locally supersymmetric, then there would be reason to ask: why this constraint? Why, if provided with the possibility to choose from the class of all super-groups, and with phase space of verified physic already being a supermanifold, why would Nature choose a purely bosonic symmetry group? It’s possible, but it shows that it is not insane to suspect that fundamentally (i.e. at high energy) it might be different.

That all said, recall again that all this is about high energy local supersymmetry (supergravity). There is no comparable argument from first-principles which would force that a theory of supergavity should settle in a vacuum where at the weak scale there is a global supersymmetry left (which is the kind of supersymmetry that is invoked for those arguments about naturalness, gauge coupling unification, dark matter etc.). In contrast, a global supersymmetry (a global Killing spinor) in a solution to the equations of motion of supergravity is about is unlikely as a global translation symmetry (of which the supersymmetry is a “square root”). We don’t expect the universe to be globally translation invariant in any one direction, even though locally it is, and analogously it would be surprising to find a global supersymmetry, even if locally everything would be supersymmetric.

In conclusion, the main question of interest seems to be a question rarely discussed at the moment:

Theoretically, the real question is: given a theory of supergravity (or some UV-completion thereof) what are the compactification mechanisms, what can one say about its effective “low” energy (say weak scale) vacua. Is there any actual mechanism, besides prejudice, that would prefer Calabi-Yau or G2 compactifications? Or maybe better: at which scale would such these be effective?

Experimentally, a good question would be: what would be experimental checks not of low energy supersymmetry, but of supergravity. For instance these authors here argue that plateau inflation (such as Starobisnky-inflation) — which is the model of inflation presently preferred by experiemtal data — gives a still better fit to experimental data after embedding into supergravity. Now, that particular argument will have its loopholes, but generally more experimental arguments for or against high energy supersymmetry (supergravity) would be interesting to have.

Urs,

You are trying to derive from an extremely general abstract theorem (that Tannaka duality works for not just groups but also Z2-graded groups) an argument for a very specific supergroup, a rather ugly one with no experimental evidence at all for it. I just don’t see any argument at all for this.

“All groups” covers almost all of mathematics, and adding in Z2-graded groups makes this even more general. I’m a big fan of the idea that quantum mechanics is fundamentally representation theory, and (see the book I’ve been writing) I think there’s a huge amount to say about how highly non-trivial and specific basic structures in representation theory govern quantum theory. But, you can’t get something from nothing: an extremely general piece of abstraction applying to almost the entire mathematical universe cannot possibly do the job of distinguishing the very specific mathematical structure that seems to govern the physical universe.

Urs Schreiber wrote: “[T]his does of course not prove local spacetime supersymmetry, but it serves to show that there are good reasons to expect that it might be: Because conversely, if the world were not locally supersymmetric, then there would be reason to ask: why this constraint?”

That’s a good question, and I cannot resist to offer a thought. Most people (including me) assume that the Standard Model (or whatever BSM model you want to replace it with) is an effective theory at large length scales of some underlying theory U. This underlying theory does not even have to be a quantum field theory. The bosonic and fermionic fields in the effective theory are effective degrees of freedom that arise in a possibly complicated way from the degrees of freedom of U. In this situation, should we expect that the effective theory allows local spacetime supersymmetry transformations that can mix the effective bosons and fermions?

I think there are essentially two possibilities we have to consider: Either there exist *many* theories U that induce effective theories with bosons and fermions that look roughly like the Standard Model; or there is essentially only one possible U with this property.

In the second case, not having any a priori information about U, I would assign a 50% prior probability (or much less, but I’ll be generous here) to the statement that the effective theory allows local spacetime supersymmetry. I.e., I would answer Urs’ question with a counterquestion: Why should this constraint *not* exist?

In the first case, however, the situation is different. If bosons and fermions can arise in many different ways from an underlying theory, we should expect that the absence of transformations that can mix them is a pretty generic property in the class of possible theories U. After all, the bosonic fields could appear effectively by a mechanism quite different from the mechanism that produces the fermions. Then we would not expect a symmetry that can mix them, because they are just quite different objects, like apples and orangutans. (In the Standard Model, the bosons and fermions do not look similar at all. I take that as a hint that they arise indeed in quite different ways from the underlying theory, whatever it may be.)

Hence, no matter whether we are in the first or (as I hope) second case or something in between, I do not find it particularly puzzling that the effective theory that describes our universe shows no sign of spacetime supersymmetry. If we would see supersymmetry, that would be an extremely strong clue about the underlying theory: it would have to induce fermions and bosons as effective degrees of freedom in very similar ways, so that the effective theory could mix them. But we do not see it. Why should anyone be surprised? For the stated reasons, I even find it very likely that supersymmetry does not occur at *any* length scale at which the effective theory is valid. And in the underlying theory, the question “Is there spacetime supersymmetry?” might conceivably not even be well-defined.

Maybe SUSY enthusiasts do not like this idea — that the bosons and fermions in our universe arise effectively from an underlying theory U in completely different ways — because they assume that then U would have to be an inelegant, complicated theory? I do not see any argument that would support this assumption.

Peter wrote:

I don’t think he’s doing that. For starters, he didn’t mention any specific supergroup, much less a specific “rather ugly one”. Which supergroup are you talking about, anyway? Whatever it is, Urs never mentioned it.

I think the only reasonable attitude is to realize that we are missing many pieces of the puzzle, both experimental pieces and conceptual pieces: that is, ideas we need, that we don’t have yet. So, people motivated primarily by mathematical elegance should not expect their work to make contact with experiment in the next few decades, or indeed at all. The time is not ripe for that. They should instead try to do good math. Good math can be recognized independent of any applications to physics, and it has its own inherent value.

I think Urs is doing good math. He’s not spending his days working on the minimal supersymmetric extension of the Standard Model or any other specific ugly attempt to ram our current theoretical thinking down the throat of the experimental data we have now. He’s instead inventing fundamental new ideas in geometry, topology and algebra – indeed, so fundamental that breaking math into these separate subjects doesn’t do justice to his work. Some of his work is on particular theories that string theorist like (showing how they fit into a single structure, the “brane bouquet”), but a lot of his work is more general than that, and thus of more general interest. I’m talking about things like infinity-categories, infinity-topoi, and how these permit a new much more general approach to old topics like Lie groups, Lie algebras, gauge theory, prequantization and so on. These are worth studying

regardlessof any application to physics. In fact, trying to connect them prematurely to particle physics runs the risk of screwing up their natural development, by making us focus on the theories we know and not on the ones we don’t.Marc Nardmann wrote:

Okay – I was trying to give examples of “supermathematics” (Z/2-graded mathematics), not supersymmetry, but I guess this was a bad example. I was in grad school in the early 1980s when Witten was starting to wow mathematicians with his new arguments for known results. His “physics proofs” of the Atiyah-Singer index theorem and positive mass theorem came out then. Both involved the Dirac operator in ways that surprised mathematicians, so I tend to mentally lump them together.

But you’re right, his argument for the positive mass theorem doesn’t use Z/2-graded ideas, at least not explicitly. Wikipedia says his argument was “inspired by positive energy theorems in the context of supergravity”, and the fourth section of Witten’s paper discusses the connection to supergravity. But he says the connection is “not altogether clear”. I don’t know if anyone ever nailed it down!

A much better example, from around the same time, would be Witten’s approach to Morse theory. I took a course on that with Raoul Bott, and at one point he said, eyebrows wagging mischievously: “So we think about this, and we get stuck. So we need to

superthink!”Around this time I also took a course from Quillen on Witten’s proof of the Atiyah-Singer index theorem. Quillen was trying to make it rigorous using “high-school calculus” and lot of elementary superalgebra. He got scooped by Getzler.

So, I think of this as the era when mathematicians realized the importance of supermathematics.

John,

I think we agree about strategy: step back and look for new mathematical insights that may later find applications in fundamental physics. Even if you don’t get what you want for physics, you’ll learn more about deep mathematics, which is all to the good. And sure, Z2-graded mathematics may very well be part of those insights. Now that I’m wrapping up work on the book, I’m looking forward to going back to doing precisely that, thinking about Dirac cohomology.

My problem with Urs is that while he’s often doing this sort of thing, at the same time he finds it necessary to try to use this to defend the central failed research program that has dominated (and done a huge amount of damage to) theoretical physics for over 30 years. His argument starting with Z2-graded Tannaka duality ends up with the specific endpoint of an argument for supergravity, in ten dimensions (whatever you want to call the local supergroup there, that’s the one I’m referring to). I don’t think there’s a serious argument there. You can’t get to that kind of specific theory from general ideas about the relation of QM, representation theory and Tannaka duality. When you try and do it, you’re just adding in lots of unexamined assumptions and eliding distinctions that are exactly the ones you need to be looking at to figure out where this train of inference goes wrong.

Defending 10d superstring theory and supergravity as the fundamental theory while arguing that any possible actual experiments are irrelevant is very dangerous, the “Not Ever Wrong” danger I’m trying to point out. Bringing very abstract not relevant mathematical statements in to help do this is a really bad idea. I think in this year we’re going to finally see the collapse of any hope that supersymmetric extensions of the standard model will ever see a test or get experimental support. I hope the community reacts to this by challenging the assumptions that led to enthusiasm for these models, not by permanently seeking refuge in excuses (“only visible at high energy”) and dubious invocations of abstract mathematics.

Peter Woit wrote: “I’m suspicious that BRST is more fundamental than people think, really needed to properly understand what is going on with gauge symmetry.”

Yes, I remember BRST seeming very ad hoc to me, until I realized I could think of the Faddeev-Popov ghosts as differential forms in disguise, with Q being essentially a version the exterior differentiation d constrained to the gauge directions. It’s been a while since I worked on this but I seem to remember convincing myself that the path integral over the ghost action expresses a coordinate-invariant volume form on the gauge surfaces like we would normally do with differential forms. Since then I’ve thought of BRST as about as fundamental and well-motivates as differential forms are.

I know there are cases where BRST gets a little more complicated and I am not sure how far the correspondence with differential forms can be taken.

John,

Wow, you’re giving me memories of grad school 🙂 That Witten paper on Morse theory was the basis of my orals, I had to present it. Honestly, could never work out what Witten was talking about until I read Roe’s book on it.

This is nothing new. Kuhn’s Theory on the Structure of Scientific Revolutions predicts exactly this sort of response. Individual scientists rarely change deeply-held views, no matter what evidence they’re faced with (as with most humans). Rather, as the evidence mounts to discount old theories and promote new ones, new scientists adhere to the newer theories while the adherents of the old theories eventually retire and leave the field. Thus, while individual scientists don’t change their views, the outlook of the field as a whole shifts over time.

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Since everyone spells these Dutch names wrong, Gerard has put up a handy web page to explain:

http://www.staff.science.uu.nl/~hooft101/ap.html

I suppose Gerard probably holds the record for having his name spelled wrong. Don’t think he doesn’t notice!

And speaking of “wrong”, wouldn’t it have been nice to see someone in the video just say “I was wrong”?

Peter wrote:

Agreed.

Not “may very well be” –

is. Let’s face it, the realization that particles with half-integer spin obey canonicalanticommutation relations, and that more generally you need to insert minus signs whenever you switch two odd objects, is precisely Z/2-graded mathematics. Z/2-gradings permeate mathematics, from Clifford algebras and K-theory on up. It’s crucial to understand them.That’s a different question from whether particle physicists should care about supergroups that mix bosonic and fermionic physical degrees of freedom. In my opinion there’s no sign from Nature that they should.

I fought hard against string theory for quite a while. I only started working on it after I gave up on fundamental physics and decided to enjoy some of the math for its own sake. So I’m a weird case. But I completely sympathize with how tough it is for people who work in the string theory community to break free of its core beliefs. I know because I broke free of loop quantum gravity.

Once you spend a few years working with people, pursuing the same majestic dream, going to conferences with them, becoming friends with them, it really feels tragic to throw in the towel and admit they’re probably on the wrong track. For a while you feel life is pointless – because nothing else feels as exciting as the dream you once had. And then you have to make a decision: you can either stay in close contact with your former colleagues and spend your time arguing with them, casting doubt on their dreams, or – as I did – you can leave them behind, staying friendly but not talking much about your new work.

So we should never expect string theorists to admit in a public announcement that they lost a bet because they were wrong. They will either succeed someday… or gradually fade away.

On a wholly separate note, not related to this supersymmetry business, I wish people would stop saying the phrase “abstract mathematics” in a critical tone of voice. Mathematics is abstract, and it’s been so at least since 1600 BC when Babylonians were solving some cubic equations. Abstraction is fundamental to mathematics. It’s good. If people said “mathematics I don’t understand”, I’d be perfectly sympathetic and try to help.

I think your real complaint has nothing to do with Deligne’s theorem being “abstract”: it’s that after applying it to see particles should form a representation of some supergroup, Urs goes the extra mile and throws in a plausibility argument that maybe, despite the experimental evidence, this supergroup should not be a mere group:

The reasoning here is hand-wavy, but the conclusion – that it’s

“not insane to suspect”the existence of supersymmetries – is so weak that I couldn’t possibly argue against it. If nobody were working on supersymmetry, I’d say we should definitely put some people on it. The problem, in my mind, starts when a research community devotes a huge amount of time to studying this possibility and not as much to studying the alternatives.Peter, for one, it’s not “Z/2-graded Tannaka duality” in Deligne’s theorem. It’s plain Tannaka duality for tensor categories in characteristic zero. That’s the force of the theorem and the point for the present discussion: Starting with something god-given that does not mention super-symmetry, the theorem says that it secretly is governed by super-symmetry.

I’ll leave it at that here. If anyone feels like discussing aspects of what I explained, let’s do so in it’s own comment thread here.

Urs said, “so why on earth would Nature then choose to constrain this possibility and have an ordinary group act on the supermanifold, if it could choose a supergroup”.

Because she is whimsical enough to dislike susy?

As forceful and mathematically appealing as it may seem, the fact that susy is now known to be nonexistent or totally out of experimental reach should suffice to abandon the idea that it (in its present form and unless miraculously proved otherwise in some foreseeably distant future) plays a key role in fundamental physics.

High energy supersymmetry (supergravity) need not necessarily be experimentally out of reach. The Starobinsky model of cosmic inflation, preferred by the PLANCK satellite data, is argued to work even better after embedding into supergravity. See here for more discussion.

John Baez wrote: “A much better example, from around the same time, would be Witten’s approach to Morse theory.”

I agree, that’s another good example.

John: “[Witten’s] argument for the positive mass theorem doesn’t use Z/2-graded ideas, at least not explicitly.”

They do not even occur implicitly. Not even the Z_2-grading of the Clifford algebra (i.e., its superalgebra structure) is used in the proof.

It’s amusing that Witten’s motivation for the spinorial proof of the positive mass theorem was a “not altogether clear relation” to supergravity. There would have been a much more natural and quite obvious motivation: the 1963 work of André Lichnerowicz about obstructions to nonnegative scalar curvature on closed manifolds. (Witten cites this work in this article, but only in passing, as an example that “spinors have been used in the past to prove various results that are at least roughly related to the positive energy theorem”.) The path from Lichnerowicz’ work to the spinorial proof of the positive mass theorem is straight and seems in hindsight hard to overlook. I could explain it here in a few paragraphs, but that might be off-topic. At least from the late 1960s on, there must have been people who knew both, Lichnerowicz’ work and the (then open) positive mass conjecture. No outburst of ingenuity would have been necessary to find the spinorial proof. It’s remarkable that nobody discovered it before 1981, and that even then the motivation was not the obvious one.

Urs,

You’re just ignoring the problem I’m pointing out, that of a huge leap of logic from this theorem to 10d supergravity. If you’re going to make huge leaps of logic, they should at least land you somewhere new and interesting.

As for Planck data providing evidence for supergravity, I’m unfortunately an expert on indefensible claims about experimental evidence of this kind, but this is a new one to me, taking this kind of claim with nothing behind it to a new level.

I’m not sure why we have to motivate mathematically SUSY when we have a very strong physical motivation to begin with.

The primary reason is that SUSY necessitates fermions and relates bosons and fermions in a deep way.

A five-year old will tell you that if you extend bosonic space-time to supersymmetric space-time you get fermions (a QM concept really) and if you make global SUSY local (as you ought to) you get gravity within the general context of Supergravity. Of course the only known way to make SUGRA UV finite is to UV complete it via String theory.

So you can think SUSY as the only consistent extension of special relativity, SUGRA as the only consistent extension of GR and String theory as the only consistent extension of QFT that can incorporate Gravity and give you Gauge Symmetry as a free bonus.

Or in another language you extend the Poincare group (SR) to Super Poincare (SUSY), the local Poincare (GR) to SUGRA and you make SUGRA consistent via String theory.

This is the bottom up approach; top down you can start with a bosonic String, follow consistency and you get the same picture and eventually the known Physics as an approximation.

Giotis, this is a tautology:

Similarly this is a tautology:

I know that some sources make advertisements of this sort, but just repeating them doesn’t make these statements less empty. Supersymmetry in physics by definition is an extension of the Poincare Lie algebra by fermions (check it out here), so of course it gives fermions and of course its local gauging gives gravity, that’s by design, not by miracle. The miracles of supersymmetry lie elsewhere.

I would like to summarize the theoretical reasons why the supersymmetric extension of Poincare algebra (SUSY) is not expected to be a correct physical theory.

1. Many people misunderstand the no-go theorem of Coleman-Mandula and Haag et al. It is a proposition for the observable symmetry, that is, it refers only to the symmetry of the physical S-matrix. Since unbroken SUSY is not realized in the real world, what we want to have is the proposition for the symmetry of Lagrangian. But nothing can be claimed for the Lagrangian symmetry; indeed, one can construct a counter-example. Thus, SUSY is not a privileged symmetry.

2. If SUSY is spontaneously broken, there must exist the Nambu-Goldstone fermion, but it is not observed. If one appeals to the super-Higgs mechanism, one must give up the important hypothesis that in the low energy region the quantum effects 0f gravity are completely negligible. If one does so, the brilliant success of SM must be regarded as merely accidental.

3. Quantum supergravity does not contain the global SUSY, that is, quantum supergravity is not a natural extension of SUSY. In classical supergravity, internal local symmetries can be easily translated into spacetime local symmetries by means 0f vierbein. But the same is no longer true for the global quantities because vierbein is a local field. Indeed, {Q, Q^(bar)} cannot have the spacetime index (mu) of the translational generator P_(mu), that is, SUSY is not reproduced.

4. In Einstein gravity, the general-coordinate-trasformation (GCT) algebra already contains not only the translation algebra but also the Lorentz algebra, that is, the Poincare algebra is a subalgebra of the GCT algebra. And the local Lorentz algebra is completely independent of it. In quantum Einstein gravity, the globalized versions of both symmetries are spontaneously broken; the unbroken physical Poincare algebra arises as a special combination just like the electromagnetic symmetry of the electroweak theory. Thus the physical Poincare algebra is a symmetry at the representatkon level. Therefore, it is quite unnatural to supersymmetrize the Poincare algebra at the Lagrangian level.

Urs,

They are tautologies of course, that’s the whole point; even so textbook tautologies are much better than often repeated, self-advertised, grandiose esoteric claims about miracles and novelties that nobody seems to pay attention to (in theoretical physics side at least)

Urs,

there are a couple of problems with the arguments from Deligne’s theorems.

First, there is some fine print that you overlook in those theorems such as group vs group scheme, and algebraic groups vs pro-algebraic groups, that means the objects can be materially different from the smooth (super) Lie groups and Lie algebras as those terms are understood in physics. It would be interesting in the non-supersymmetric case to understand whether this more algebraic type of structure, such as a group scheme, is useful anywhere in the physics, and also whether the theorems like Deligne’s hold in smooth or complex-analytic settings.

Second, the standard model (and most other non-SUSY QFT) uses an ordinary, non-supersymmetric, finite dimensional, gauge group, but some of the irreducible representations of that group are fermions. Having fermions in the theory therefore does not imply anything about the group being Z/2 graded. Deligne’s theorem tells us that supergroups are complicated enough to accomodate any experimentally observed tensor product rules for particles (i.e., irreducible representations). To make a case for supersymmetry using Deligne’s theorems, you would need some no-go theorem for ordinary Lie groups, explaining what limitations on the allowed sorts of tensor products are imposed by the absence of SUSY.

On topic: other SUSY bets. In particular Lubos Motl and Gordon Kane. I note that the two LHC main detectors are now both above 25 inverse fb for this year. That adds up to above 50, plus the bits from last year. Lubos’s bet says 30, but does that mean combined detectors or just one? You (Woit) quote Kane as saying 300 inverse fb, but Tommaso Dorigo quotes Kane “Now that we can predict the gluino mass from compactified M theory we know that superpartners should not have been expected in LHC Run 1 because the gluino mass is about 1.5 TeV, and it will appear in Run 2 once the luminosity gets over 15-20 fb-1.” which while not a bet is a very confident numerical prediction.

At a total of over 50, despite the total lack at the recent meeting, the analysis people and their stable of leakers would surely have leaked something as important as a SUSY-ascribable bump.

Presumably CERN has computerized autoanalysis constantly updating the

data plots and their bump standard deviations.

Doug McDonald,

A problem with many of these bets is that they were made before the LHC turned on, and ran into trouble, forcing Run I to be at lower (8 TeV) energy. So, the people on the SUSY side of the bet might argue that only the data at full energy should count (actually, design energy was 14 TeV and they are running at 13 TeV, but nobody thinks that difference matters).

Putting together this year and last year’s data, they’re at about 30 inverse fb of 13 TeV data. So, when this data is analyzed, Lubos’s bet is lost. I gather he’ll hang on and not give up for a while, since there are lots of ongoing analyses. No, I’ve heard no rumors of SUSY signals in Run 2 data.

That “prediction” of Kane’s is just the latest one in a long list of falsified ones. He’s never in the past acknowledged that a prediction being wrong has any implication for the theory he is pushing, don’t see why he should start now.

Another thing about the argument for SUSY using Deligne’s theorem(s) on tensor categories is that Deligne refers to bare linear representations whereas the representations used to represent elementary particles involve unitary or projective structure on the representations, or positive-energy conditions.

OK, one might think that if supergroups are enough to accomodate general categories of finite-dimensional linear representations, then any extra structure on the representations must come from some extra data decorating the supergroups, in a way that would not change the basic idea of supergroups being the structure dictated by tensor categories. But having such a straightforward picture is only a hope, not something that would have to occur. Or if it does occur, the extra data could beef up the supergroups into more exotic categories of objects that we were hoping to avoid (as a flight of fancy to illustrate the idea: take a quadratic form to give the unitary structure, from that try and construct a Poisson bracket, which happens to be deformation data to form a quantum group… and if that is too constrained then deform in the even more exotic quasi-quantum category).

It is easy to glibly think of super Lie groups and algebras as some sort of next-more-complicated thing after Lie groups, but they are actually qualitatively more complex and Deligne’s theorem is an indication of that. Another one is that the finite dimensional simple Lie superalgebras are not classified by discrete data, there are continuous moduli for some types of them.

p.s. In the preceding comment I wrote “gauge group” where I should have written (super)Poincare group, which is the thing whose representations are particles that are tensored together. But the same point applies, that having fermionic things among the representations does not by itself imply Z/2 grading.

Urs,

while I sympathize with your standpoints, in full contrast to other’s,

for sake of correctness I need to point out that your statement

“….) just so happens to be 2d supersymmetric (and called the “superstring” only once this was realized), which in turn is interesting because it miraculously implies that the effective spacetime theory of which these strings are quata is locally 10d supersymmetric..”

is misleasing if not wrong, despite it has been claimed so for zilli0ns of times.

Take as counterexamples the “other” 10 dim string theories that are not spacetime susy inspite of having world-sheet susy. Eg the heterotic string with O(16)xO(16) symmetry.

These theories are almost never mentioned when talking about the grand scheme of things, for some reason.

On Dine’s quote… it is buried in a popular article, certainly it is not the banner headline… even the 2 sentences before are: “Despite those successes, good reasons exist for skepticism. Some are experimental: Apart from coupling unification, no direct evidence yet argues for supersymmetry.” Not denying that Dine went overboard in the next sentence, but I don’t think that quote is a main thrust of the article, or, within a light year of the consensus view of the experimental particle physics community.

Just have to go back a few months in Physics Today for a sober article by Fabiola Gianotti and Chris Quigg… quoting from that one “theorists have advanced many extensions of electroweak theory—supersymmetry and technicolor, for example—that compel additional new phenomena near 1 TeV.” They get totally right, 4 or so years in advance: “An essential first step toward decoding electroweak symmetry breaking is to find the Higgs boson and learn its properties. One promising channel for an early discovery is H → ZZ → 4 charged leptons. Backgrounds are very small, so even a handful of events would suffice for a claim of discov- ery. Establishing the signal will require efficient electron and muon reconstruction and identification down to a few GeV.”

On Kane, “That “prediction” of Kane’s is just the latest one in a long list of falsified ones. He’s never in the past acknowledged that a prediction being wrong has any implication for the theory he is pushing, don’t see why he should start now.”

Well, I’ve heard him acknowledge just that many times. He is an honest guy. I don’t really understand what data you have used to support such a strong statement.

I can’t think of any useful reasons to beat up optimists, except if they have directly suppressed good science. I don’t think Dine and Kane have done so; optimists generally don’t suppress good science, they encourage too promiscuously.

Their enthusiasm has pushed the field forward, and the personal embarrassment they suffer from wrong predictions is a sociological issue, and irrelevant for getting good physics done. If any thing, making predictions that prove to be wrong and that embarrass in the long run is helpful to the progress of physics…. the right idea might well eventually be stimulated by the wrong prediction.

Only in retrospect does physics seem to be sort of linear… the advance of physics is always more like diffusion, with lots of backward and forward motion. Sideways too. Overly enthusiastic ideas are just part of the diffusion process.

GoletaBeach,

One problem with writing a prominent article/book saying “SUSY will either be discovered at the LHC or is wrong”, and then refusing to acknowledge that SUSY is wrong when the LHC doesn’t see it is that you destroy your own credibility if you do this. Kane already has passed the point where anyone thinks his “predictions” are credible, and while Dine has been more circumspect, if he tries to make more such claims about SUSY at higher energies, few will take them seriously.

Unfortunately, when this kind of behavior is widespread, it becomes a problem not just for certain people’s credibility, but for the general credibility of the field, and that has serious implications. In another comment thread, someone pointed out that CN Yang has publicly come out against the proposed Chinese collider. One of his main arguments is that SUSY is being put forward as a reason for building such a machine, and that this motivation lacks credibility. He’s probably aware of pre-LHC arguments like those of Dine and Kane, not willing to tolerate them any more, and this will have implications for those trying to make the case for a new collider.