unknown1111 said:
I'm currently doing my PhD in theoretical particle physics. I understand SUSY, the Poincare Group and Wigner's Classification quite good. I've read the article twice. However I have no clue what the author is talking about.
To me it reads like the usual SUSY propaganda: SUSY must be correct, because otherwise string theory is in deep trouble. Thus let's find some good sounding reasons why SUSY is inevitable.
This article seems motivated by the current doomsday mood in the HEP community. Everyone was certain that SUSY shows up at the LHC, just as everyone was certain that SUSY shows up at LEP or the Tevatron. (And sure, the 100 TeV collider certainly will find SUSY.) Howecer, there is no experimental evidence for anything beyond the standard model and certainly no signal that hints towards SUSY particles. The fact that the LHC did not find any SUSY particles is a big problem for SUSY fans, because now one main motivation is no longer valid (SUSY as a solution of the naturalness problem).
Therefore, SUSY isn't very attractive anymore. There are four main motivations for SUSY:
Solving the naturalness problem (Higgs mass problem)
Unfication of the three standard model forces. However this argument is rather weak, because any BSM theory with as many free paramters as SUSY can be easily fitted such that the couplings unify. In addition, it's quite unlikely that a big unified symmetry (SO(10), E6) breaks directly to SU(3)xSU(2)xU(1). Instead an intermediate symmetry group between the unifcation and the standard model group, like the Pati-Salam group possibly exists. If this ist the case the couplings ALWAYS unify with SUSY or without.
Solving the Dark Matter problem. This argument is rather weak, too. Any expansion of the standard model with additional particles contains a dark matter candidate if we impose an additional discrete symmtry to guarantee its stability, which is what SUSY does.
The Coleman-Mandula-Theorem and the argument that SUSY is the only possibility to mix spacetime and internal symmetries. I've also problems with this argument, but this comment is already too long. In short, I don't think that SUSY helps to understand why fermions and bosons behave so differently (which is one of the biggest mysteries in modern physics), because this difference is simply the assumption at the start of SUSY. Thus I don't see which theoretical problem SUSY solves or why the proposed "unification" of spacetime and internal symmetries helps in any way.
Now the first one is no longer valid. The second and third are very weak arguments anyway. Thus it is not suprising that many SUSY researches are stopping to work on SUSY topics now. However there is a group of researches that can not stop and thus needs to find new motivation for SUSY: string theorists.
This is how we end with an article like this. Lots of highbrow mathematics and complicated wording, which impresses students and laymans and leaves the impression that SUSY is inevitable.
[URL='https://www.physicsforums.com/insights/author/urs-schreiber/']Urs Schreiber[/URL] said:
No. The article presents a fact that was discovered by somebody with no interest in supersymmetry, either way.
Most of what you quote are standard arguments for unbroken low-energy susy. As explained in the article right at the beginning, this is not what it is about. Remains the Coleman-Mandula theorem, on which the article comments in some detail towards the end.
Try to read it. Try to read it without ideology. It is an exposition of a mathematical theorem, which you may try to understand and accept, but which does not go away by becoming angry at it.
um his argument was on *broken* low energy SUSY. not unbroken. and in your account SUSY still has to be broken though obviously at a higher energy scale than what LHC can find.
mathematician Deligne may not have had a personal interest in supersymmetry/string theory, but it seems clear that strings/susy is your own personal belief and research interest and by you i mean Urs schreiber.
peter woit's assessement
http://www.math.columbia.edu/~woit/wordpress/?p=8708#comments
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.
and
Peter Woit says:
August 29, 2016 at 10:27 am
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 into 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.