The first time I went to a lecture on supersymmetry the auditorium was so packed that many people could not get in. I was pleased I had anticipated the high demand and arrived very early. In his talk entitled “Is the End in Sight for Theoretical Physics?” The speaker explained to us that supersymmetry was the greatest hope for theoretical physics because it offered the possibility to unify the gauge theories of particle physics with a quantum theory of gravity in a way that might avoid the infinities of quantum field theory.

The speaker was of course Stephen Hawking and the occasion was his inauguration as Lucasian Professor in Cambridge. The version of supersymmetry that had him so excited was N=8 Supergravity in 4 dimensions. Cautiously he predicted that a complete theory of particle physics could be worked out in 20 years time using this new superunified theory.

30 years have passed and we know that things did not work out quite as Hawking has hoped. He thought that N=8 supergravity might be a unique candidate for a fully unified theory of physics, although the particles we now know as fundamental would have to be composite. He did not consider higher dimensional theories because he thought that details such as the number of spacetime dimensions could be explained by anthropomorphic arguments.

A few years later, supergravity was replaced by superstring theories and higher dimensions became mandatory. The underlying theory still possesses a similar uniqueness but now anthropomorphic arguments are needed to select the real world vacuum from a vast landscape of possibilities that superstring theory offers. Hawking has now retired as Lucasian professor to be replaced by one of superstrings’ pioneers, Michael Green*.* Supersymmetry and superstrings face a skeptical backlash from a large section of the younger generation who are disillusioned by its failure to provide clear predictions for particle physics or cosmology after so much time.

Now the table may be turning full circle and this time support for supersymmetry comes not just from theory, but from experiment too. The version of supersymmetry that has come to the fore is the Minimal Supersymmetric Standard Model – an extension of the well established Standard Model of particle physics that includes an additional broken supersymmetry. This leads to one superpartner for every familiar particle that we know already, plus an alternative Higgs sector with fives Higgs particles, two of them charged.

The MSSM first appeared just a year after Hawking’s lecture. Since its early days it has been understood that it improves the naturalness of low energy particle physics due to anomaly cancellations that help keep the Higgs sector light. With the addition of supersymmetry the three running coupling constants converge at one energy point, suggesting a dessert of new physics up to a more complete unification at the GUT scale. The model also provides a natural R-parity symmetry that would make its lightest particle stable. This offers a unique candidate for dark matter whose stability would otherwise be very hard to explain.

For the last decade or perhaps more, theorists have been anticipating the imminent discovery of supersymmetry in the world’s highest energy particle accelerators. Fermilab was thought to have a chance of discovery with the Tevatron and there were even some false starts that faded away as the statistics grew. Now their hopes turn to the Large Hadron Collider but the Tevatron is not finished yet. In recent months we have seen some tantalising results reported by Fermilab that support the MSSM. Nothing is conclusive yet, but the combined evidence all seems to point in the right direction.

For those of us who grow up with the idea that supersymmetry is the final move in a game of unification that leads inevitably to a complete theory, these reports are too hard to dismiss. After the ICHEP conference we drool over the results that should have been shown, but weren’t. Plots which show inconclusive signals of less than 3-sigmas statistical significance are quick and easy to approve for publication. They don’t lead to big headlines. Anything above three sigmas would count as an observation and that puts it in a different league of results. With some history of failed observations from the past, Fermilab are likely to put off publication until the next round of data is seen to add rather than subtract from the result. For us the outsiders, the mere absence of certain plots starts to look like a sign to get excited about.

For the supersymmetry skeptics the conclusions to be drawn are different. Any signal below 3 sigma is to be dismissed as noise. They can even dismiss the exclusion of the Higgs mass range that now strongly supports a light Higgs sector as predicted by supersymmetry. It is indirect and still inconclusive.

If supersymmetry is indeed just below the surface, what will happen next? The Tevatron will continue to analyse the data they have while collecting some more until about 2013. The signal will grow until it is clear that something new has been seen. The LHC will not have the luminosity to see the low mass Higgs sector before the Tevatron, but supersymmetry will offer other new particles of higher mass. The LHC might pick out some of those very quickly and start to study their properties. Very soon the parameter space of supersymmetric models will be narrowed down. There will be a huge spurt of activity amongst theorists as they figure out how particle physics works at this scale. If there really is a desert of new physics beyond supersymmetry it may be possible to work out a convincing scenario for physics right up to the GUT scale. Possibly the next generation of accelerators will be needed to pin down most of the coupling constants. If they are clever enough, there may be enough information to figure out the mechanism for breaking supersymmetry at the GUT scale. That could reveal a perfectly supersymmetric world at higher energies with far fewer free parameters.

It will not stop there. If supersymmetry is part of gauge field unfication then its unbroken gauge form will include supergravity. The experimenters will have had their day again as theory pushes into higher energies with renewed confidence. How far it will run is hard to say but the connection between supersymmetry and quantum gravity is hard to pull apart. Knowing the details of supersymmetry at the electroweak scale could be enough to lead us to the end of theoretical particle physics in the sense that Hawking predicted 30 years ago. Perhaps even superstrings will suddenly look right again. Until we have the next results from experiment we cannot be sure, but that is what makes the current situation so exciting. In just a few years – perhaps even just months – a renaissance of particle physics merging experiment and theory might be well underway. It might pan out in a less predictable way than I have suggested here, but it is sure to be revealing, if it happens at all.

**Update:** see also the discussion on Lubos blog, and of course his many detailed pages extolling the virtues of supersymmetry.

Why this turn?

“Anything above three sigmas would count as an observation” – unbelievable!

Why could it not then be shown? Some competition? This stinks (money).

That greek has predicted that a lighter Higgs would need a sigma over 6, a heavy higgs over 18! And now 3 would do?

A 3 sigma result is called an “observation” but they need 5 sigma to call it a “discovery”. That is just the conventional terminology for experimental particle physics.

An “observation” is not considered as definitive as a “discovery”, but it is worth publishing as positive evidence that an effect is there.

Because of this convention a lab may chose not to publish a 3 sigma result if they have a chance of improving it to claim a discovery in the near future. A 3 sigma effect is going to be overstated by the press and scrutinised by peers who might complain about possible systematic errors. When the analysis is complicated it may be prudent to wait for a clearer result before publishing. Comeptition will tend to have the opposite effect of making them publish quicker.

Excellent article, Phil. So far, I have considered my TRF blog to be the only well-known website in this Solar System that openly advocates SUSY as the likely outcome of the near-future HEP experiments.

Even though your defense of this attitude is a little bit late and looks a little bit opportunistic, it’s still true that if and when SUSY is found, you surely deserve at least a little footnote, too. ;-)

Well I have not been running this blog for very long but I may have said a little bit about supersymmetry before, e.g at http://www.karlin.mff.cuni.cz/~motl/Gibbs/symmetry.htm :)

That’s really “before”, 1996 – and the date is probably just a date of my copy; yours was probably older. :-)

Thank you for a nice article directly form heart. I hope do not irritate readers too much with my personal reminiscences.

I remained very long skeptic about space-time supersymmetry since the extension of space-time by Grassmann parameters looked to me so ugly and formal and still does so. I am also convinced that super-string approach to supersymmetry with Majorana spinors is a fatal mistake. And of course, in my personal Universe the separate conservation of B and L simply does not allow the introduction of supersymmetry as it is done in SUSY and string models.

I however regarded super-conformal symmetry in my primitive mathematically uncivilized manner something which is a must. The formalism in that vague sense that I have been able to develop makes it possible to formulate it geometrically in terms of the spinor structure of the “world of classical worlds” possessing Kahler geometry. Contractions of gamma matrices with isometry generators and Hamiltonians of symplectic isometries would define one instance of a super algebra but super-algebraization seems to be much more general: something analogous to the extension of real analytic functions to complex analytic ones. WCW gammas would be represented in terms of fermionic oscillator operators of second quantized induced spinor fields satisfying the analog of Dirac equation (roughly speaking).

During last year it became clear that the analog SUSY as QFT limit might make sense after all although I cannot have Majorana spinors. The algebra is spanned by the oscillator operators of spinor modes associated with light-like orbits of partonic 2-surfaces. The problem how to avoid Majorana spinors has been really painful and involved a lot of self cheating but I believe that this problem has found the final solution or at least the last one that I am able to invent with my aging brain;-). The construction of QFT limit made clear that this symmetry could be extended to N=infty SUSY but with different interpretation. This if the number of spinor modes associated with the orbit of partonic 2-surface is infinite. In any case, the number of superpartners behaving as ordinary massless particles would be finite.

This was not the end. It became increasingly clear that

finite measurement resolution is an inherent property of dynamics and reduces in fundamental theory SUSY to finite N SUSY with super generators assignable to the points of braids defining end points of stringy surfaces. N=1 SUSYs would emerge naturally as a broken symmetry and would due to right handed neutrino having very weak interaction with other particles. Everything would be broken from beginning.

So: suddenly I feel that I am not a total outsider to the main stream anymore. What a relief! I belong to society! I also began to realize in my primitive and half-conscious manner how incredibly beautiful the notion of supersymmetry is. Higgs mechanism is something which I will never eat but SUSY understood in general enough sense is talk of God.

All this is of course misty and half-baked but I am now a true believer absolutely convinced that SUSY in some form is bound to show itself in its full glory to the suffering mortals sooner or later;-).

Dear Matti, holy crap. What’s wrong with the Grassmannian variables? In the path integral approach to QFT, they’re as necessary to describe the fermionic fields (such as the electron field which is pretty important, believe me) as normal commuting variables are necessary to describe the bosonic ones (such as the electromagnetic field).

And what’s wrong with the Majorana fermions? They’re just a spin-1/2 representation of the Lorentz group, with a reality condition – something that obviously exists mathematically and is consistent physically (in dimensions such as 3+1), according to all rational criteria of consistency. It follows that whatever notion of “ugliness” you use, it’s damn guaranteed to be irrational.

You know, I kind of know where you’re coming from. When I began to study string theory, I thought that e.g. open strings were ugly because they still had the singular end points, just like the point-like theories, and so on. However, when I learned everything that was needed, it became very clear that theories with open strings may be exactly as consistent as theories without open strings (with closed strings only).

In fact, nonperturbatively, every type I/II-like theory may contain D-branes which inevitably carry open strings as their excitations. It doesn’t matter that the world sheets have boundaries. The infinities and anomalies are gone for type I – and other theories with lower-dimensional branes.

Well, I have never considered Grassmannian variables ugly. It’s just stupid. One misunderstands – or is ignorant about – these variables up to some point in his life. Once he understands them, he must be completely sure that as quantum variables, i.e. as integration variables in a path integral, they’re exactly as consistent as the commuting variables. Omitting them is the same mistake as omitting the solution “-1″ of the equation “x squared equals one”.

In the same way, once a person understands the representation theory of Lie groups, he must know that vectors, just like tensors, scalars, Majorana spinors, any other spinors, or e.g. pornographic spintensors are just equally OK as long as the group theory works. And it works. Only different, more detailed physical criteria may pick one representation and disfavor another.

So in my opinion, what you’re writing about your negative emotions against various mathematical structures (and, holy cow, even things such as the Higgs mechanism or unbroken SUSY) proves that you have either not understood what they mean at all, or that your brain is dominated by completely irrational Al Gore Rhythms.

I agree completely with the first sentence of Lubos. Matti, you always surprise me. But all these mirrors would perhaps be a SUSY too, but a different kind of SUSY?

Georgios Choudalakis has done his thesis on possible new physics, and MSSM is one possibility, but there are others too.

Lubos must be very happy in his ‘heaven of dreams':) I hope this would make him more humble :)

It’s the biology. I’m more convinced now. To find the answers you physicists must look at the ‘proofs’ in biology and condensed matter physic. It must be included. It is no parenthesis as Lubos claims.

All experimental facts must be able to include and explain. It is Gods talk :)

[...] high-energy physics“), que toma título de de y comenta a la entrada de Philip Gibbs, “Suzy at Last?,” viXra log, July 30, 2010. ¿Se observará la supersimetría en el LHC del CERN? La [...]

Was “dessert of new physics” supposed to be “desert”?

Normally, spelling nitpicks are pretty pathetic; but in this case the alternative arguably means the opposite, with desert conveying a “dearth” or featureless wilderness, and “dessert” a feast of juicy appetizing morsels ;-)

Let me explain again :) There may be a desert of physics between the weak and GUT unification scales, but this means you get a dessert because you can extrapolate from what we discover experimentally at the weak scale up to the GUT scale and figure out theoretically how symmetry breaking works there. Clear now? :)

Actually the worst typo was that I wrote Suzy when I meant Susy and nobody said anything.

Dear Phil, I thought that Suzy was a proud source of your idiosyncracy, meant to be closer to Suzanne, so I even copied it as my title although I would never use this thing myself.

I can confirm that when you in Sahara, desserts are very juicy.

I’d like to think it was something deep and meaningful arising from my subconscious, but in truth I’m just a little dyslexic. Sometimes I try to use permutation invariance on letters.

Thanks for posting this information Phil. This is a very interesting conversation by the way. People seem to think that Dr. Motl is some kind of stubborn carmudgeon, but I have a feeling that both you and I already knew otherwise a long time ago.

I think that this conversation (and the accompanying post on his blog) will convince everyone else. I mean, not that it’s likely that Dr. Motl would really care either way, but that’s part of his charm. :)

And, of course, I think you know what your work (event symmetry, vixra.org, etc, etc) means to me, even if you do not care either way.

Thank you.

Looks like Physicist are all lost, why wait for some so-called high profile physicist to announce that SUSY is the way to go?? I think we are getting it all wrong. Each of us must find their own path, independent of what S. W. Hawking, E. Witten or some mortal has to say.

We are putting authority over truth here! Lets all chant our way and compare these paths to our immediate reality. I want to say, unified will not occur in the minds of a many physicists, but in the mind of one individual. They will see the picture, the whole picture and they will write it down. God won’t give the picture in bits to many, but to one individual, this I am sure of.

So, let get to business and try to finds the unified theory.

Golden.

What I am looking for is some neutral discussion on this – no Susy-heaven or Susy-hell.

It seems quite odd to me that it could be possible that a whole world of mirrors could have remain unseen for so long. Something must have been seen. Either are we bad at looking or it is a fantasy.

If the inflation model is wrong maybe the high energy is not the right way. Maybe we should look for similarities instead? What I see is oscillating pairs everywhere, but is Susy right way?

If we first started to see what mass is in reality, maybe then we could better know what we are looking for?

Golden Hi, I dont think any of us are excited about SUSY just because Hawking or Witten like it. We are looking at the evidence in its favour, both theoretical and experimental. Most of that evidence has come from people less well known but it does not matter who says it. What counts is how good the evidence is. If I accepted everything Hawking and Witten ever said I would be looking for primordial black holes, cosmic strings and no Higgs, but I am not. A few people are, but usually because they see some sense in the ideas, not because of who said it.

Ulla, We may have seen this mirror world in the form of dark matter. I am sure you know that in the accelerators anything that has a mass too high or an interaction too weak will not be seen until we build one powerful enough. There could easily be more unseen than just supersymmetry but we have other constraints from bounds on nucleon lifetimes,cosmological observations etc. It is not easy to build alternative models that fit the facts and appear natural.

Nevertheless, SUSY could be wrong, there are other ideas that may be less well motivated but could still be right, or theorists could have missed a great idea that works. Perhaps there is one lone person out there with the right idea and noone is listening. Until we have a clear experimental observation there is a chance that SUSY might be a theorists fantasy. I dont know anyone who thinks otherwise even if some people now estimate the odds to be very low based on what we know already.

Ok Phil, I get you.

For a more pessimistic view on SUSY see for example:

http://www.math.columbia.edu/~woit/wordpress/?p=3082#comments

If LHC continues to run as planned, we ought to have pretty firm indications a way or another by the end of 2011 or 2012.

Ervin

2012 will probbaly be too soon to rule out much at the LHC, but it could easily be soon enough to discover something. We need more luminosity and possibly more energy and that could take until about 2016. Maybe I’ll write a post about this.

Dear Ervin, I can’t open the page above because my browser complains about a critical security threat. But the sentence you wrote – not sure whether it’s yours or you quoted Peter Void – doesn’t sound too sensible because the LHC will be stopped throughout 2012, so if it doesn’t find things before the end of 2011, it’s pretty unlikely it will before the end of 2012.

Phil and Lubos,

It would be informative if you could map out the time-frame for finding SUSY based on the LHC schedule, anticipated decay channels/cross sections and the anticipated spectrum of SUSY masses.

Cheers,

Ervin

Ervin, that is not a bad idea. The parameter space of supersymmetry is too big to cover every eventuallity, but it would still be instructive to work out a typical example to see how things might unfold. I would have to do some homework to come up with something, but if I have time I will.

[...] in high-energy physics“), que toma título de y comenta a la entrada de Philip Gibbs, “Suzy at Last?,” viXra log, July 30, 2010. ¿Se observará la supersimetría en el LHC del CERN? La signatura de [...]

[...] in high-energy physics“), que toma título de y comenta a la entrada de Philip Gibbs, “Suzy at Last?,” viXra log, July 30, 2010. ¿Se observará la supersimetría en el LHC del CERN? La signatura de [...]