# In case you are not a fan of the idea of SUSY, what bothers you about it?

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## Main Question or Discussion Point

I am not talking about superstrings, but the idea of supersymmetry itself.

Let me say what annoys me. I will put aside the advantages of it satisfying Coleman-Mandula theorem or solving the instabilities of the Higgs field, lorentz invariance or any other consistency that it satisfies in specific theories. I will just say about the aesthetic part, what makes me feel it is something ugly by iteself.

3 alternative ideas:

1.If you are going to try to unify the idea of bosons and fermions, I would like to see a geometric origin in an object in which different eigenvectors would yield different statistics.
2.I think the idea of super partners quite boring. Why not composite particles sometimes? For example, the super partner of a fermion would be a composite of 2 fermions of the same kind instead of a boson.
3.Why not letting the whole continuum of spin values. Maybe the object in 1. could have special regimes in which spins other than 1 and 1/2 would be allowed.

What about you people, that also don't find beauty in SUSY?

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arivero
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Do you want a geometric origin or a classical picture? A not very obvious thing is that SQFT multiplets are pretty because they are put with $\hbar=1$. Put the hbars, consider the classical limit, and suffer the consequences of the spin-statistics theorem: You can accumulate bosons and then produce an infinity to counterweight the limit of hbar going to zero.

My geometrical "feeling" is that bosons produce space, while fermions can produce points. Or bosons are currents, fermions are forms. Os something so.

With this feeling, it is worse in string theory. Because of the picture of a fermion as an extended object.

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1,2 and 3 are alternative ideas.

For example, you talked about idea 1. In that case, I would like a geometrical picture, not classical. And I am not even thinking about strings. I am thinking really about things that I don't like about supersymmetry. Suppose some crazy space with crazy objects where in the low energy limit you'd get bosons and fermions as its eigenvalues.

arivero
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Well, as you probably know, I am a strong supporter of idea 2 and I have argued that the standard model provides a supportive argument because three generations and a massive quark is the only way for an SU(3)xSU(2)xU(1) content to bootstrap itself.
Moreover, the first reaction of Schwarz, in his papers of 1970, to the Ramond fermion was to suggest idea 2. It seems that the idea was abandoned soon, but I havent found explicit criticism in the literature, just notes of discomfort.

Following with idea 1, probably it depends of how flexible you are for the definition of space. The point is that each component, depending of spin, has different units. So a manifold it will not be. It could be something along, and beyond, the trajectory that goes from phase space to cotangent fiber bundles. The naivete here is that the units in phase space have a inverse relationship, x p = 1, while the units in supersymmetry seem to enjoy a particular polynomial closure, the product of two fermions is a boson.

I guess that a lot of geometric constructions could work for global supersymmetry; the operator going from fermions to bosons is not far from one of the operators changing homology to cohomology and then back. But when you consider local supersymmetry, such visualisations explode, perhaps because they inherit from the aformentioned naivete.

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What is bootstrap?

Merriam-Webster Dictionary Results: bootstrap
3 results for: bootstrap
Main Entry: bootstrap
Function: transitive verb
Date: 1951
Results: to promote or develop by initiative and effort with little or no assistance - bootstrapped herself to the top.

arivero
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What is bootstrap?
Bootstrap is one of the pieces in the origin of dual models. An argument to clasify the poles of the S-Matrix, in a way that implied that each particle could be considered as a sum of composites of all the others, or something so. See
http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+K+BOOTSTRAP+AND+DATE+BEFORE+1975&FORMAT=www&SEQUENCE=ds [Broken]
to get an idea of the popularity of the argument. Remember that Veneziano "dual amplitude" is from 1968, and its interpretation as an string was only two or three years later. Also, Ramond fermion is from 1971.

I am not sure if bootstrap is the subject of any thread here. sBootstrap is my own argument that, if we consider that the number of supersymmetric scalarFermions of 3 generations of the standard model coincides, charge by charge (and both for leptons and quarks) with the number of combinations of the 5 light quarks of the standard model, then supersymmetry provides the same kind of closure of the bootstrap spirit: no new fermions in the composite structure, simply the same ones.

My part on sBootstrap is the closure. The "idea 2" here, that the fermions in the Ramond-Neveu-Schwarz dual model are the quarks and thus supermultiplets are mixed of elementary and composites, is proposed by J. H. Schwarz himself, in Dual quark-gluon model of hadrons, Phys.Lett.B37:315-319,1971.
(albeit it is already mentioned in the last parragraph of a previous article with Neveau.)

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arivero
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3.Why not letting the whole continuum of spin values. Maybe the object in 1. could have special regimes in which spins other than 1 and 1/2 would be allowed.
If spin is related to the rotation group (and angular momentum is), then only integer and half-integer values do exist. I suppose that the only way out is to allow for a theory of group representations over vector spaces with fields different from R and C; tell p-adic, archimedian or some strange beast. Of course space dim >=2, for the rotation group to be continuous. So supersymmetry in the string worldsheet is, as MTd2 has stressed in other threads, a different question. But 3+1 world is the thing we have.

So the point is reduced to "should a theory allow for fundamental entities of all the spins 0, 1/2, 1, 3/2, 2, 5/2, ... ?

Edit: it seems (eg see Weinberg's book) that the build of creator and annihilator of particles of spin N asks for tensors in representation (N,0)+(0,N) or greater, which makes tensors with 2N indexes and antisymmetric in a set N of them. I am not very sure of how it works, because for gravity (2,0)+(0,2) is the curvature tensor Rijkl, but the field really is the graviton, with only two indexes, probably because we want the force to be long range and then we impose the additional constrain of being massless. In any case, if the tensors become trivial beyond some number, it is an argument to stop the series, the limit depending of the dimension of space. Actually, when you compactify D=11 sugra, a three indexed field disappears when coming to D=4. And one step beyond, in D=3, the graviton itself disappears.

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marcus
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Dearly Missed
What is bootstrap?
Originally it comes from a kind of joke----a kind of folk humor.

The straps on a boot are like the strings on a shoe---the shoe-strings.
The idea is that a man could pull himself up into the air
by reaching down and grabbing his own shoestrings
and pulling himself up by them.

In the folk expression it is immediately seen to be impossible---an absurd paradox.

As if you could levitate by reaching up and grasping the hair on your head, and pulling upwards. Or could propel yourself in a train by pushing against the seat in front of you----or propel yourself in a sailboat, when there is no wind, by blowing into the sail.

However think of the example of a universe which brings itself into existence from a quantum fluctuation of almost zero energy. Suppose the negative gravitational energy of the potential well which it creates is exactly balanced by the positive energy of material existence. In that example the universe seems to have pulled itself into existence "by its own bootstraps".

bootstrap: to promote or develop by initiative and effort with little or no assistance - bootstrapped herself to the top.
I took it too personnaly (as a blame) and removed my answer with my pet theory where fermionic and bosonic eigenvectors are joined in one compound system.

arivero
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I took it too personnaly (as a blame) and removed my answer with my pet theory where fermionic and bosonic eigenvectors are joined in one compound system.
Ah no, it is only an unfortunate term, from the sixties or perhaps the late fifties. In SPIRES, the search FIND K BOOTSTRAP find 1302 articles.

I think that in susy all the generators are fermionic, in the sense that any bosonic state, beyond the vacuum states, can be reached by using the fermionic generator, can it?

(Edit: hmm, not exactly true, because Kaluza Klein generates new bosonic states. Actually it is amusing that compactification should generate some new bosonic states and their partners, so it is a clue to clarify the geometry of susy)

When I was a student (1975-81), the super-symmetry was developing fast. I made even a work on super-gravity in the De Sitter space with V. Soroka, a D.V. Volkov's collaborator. There was a hope to "cure" infinities in SuSy approach, following the work by Wess and Zumino. This and many other ideas failed, so I have a sceptic attitude to everything in the theoretical physics which is not motivated physically/experimentally.

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I was thinking something stringy, let me know if you've heard something about this. Suppose you have fluxes, organized as closed loops, or strings. Let each loop have a charge quantity which is proportional to its rotation.

Now, suppose that this charge is quantized. I can try to guess that the 2 basic movements are 1 strands orbiting and 1 strand self orbiting.

1 strands orbiting would yield +- 1, +- 2,... spin particles for each particle. ( there is no 0 flux)

1 self orbit would require a strand tying itself in the surface of a Klein Bottle, so that any flux could be arranged to feel an equal self charge. Now, to complete a complete turn, each charge would take twice the speed and so twice the charge, even because, well, it's 2 strands for the price of one. If the kinetic energy is converted in the spin of a simple strand, it would yield values of 0, +-2, +-4. 0 here is possible, because of the paralel translation in that surface. Note that I can align as many as self stranded I want here that there won't be influence on the self flux of others.

Also, note that the first case is similar to the case of a fermion. The second is similar to the case of a boson.

Note that the strand that makes up this boson must be 4 dimensional and non local, given that it would otherwise make short closed time like paths.

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If spin is related to the rotation group (and angular momentum is), then only integer and half-integer values do exist. I suppose that the only way out is to allow for a theory of group representations over vector spaces with fields different from R and C; tell p-adic, archimedian or some strange beast. Of course space dim >=2, for the rotation group to be continuous.
John Baez figured out a way to do such kind exotic statistics in 4 dimensions!

http://arxiv.org/abs/gr-qc/0603085