# Super symmetry?

Well, I've really been getting into Quantum Relativity and Quantum physics, and one thing really just seems fuzzy to me.

Super Symmetry.

Wikipedia goes into too much math and history and blah blah blah...

Other sites just say the history of discovering super symmetry

Some sites are non-descriptive and talk like super symmetry is just shadow particles.

But overall, I just DON'T GET WHAT SUPER SYMMETRY IS, AND WHY WE USE THE THEORY.

Can someone PLEASE explain the reason we factor in super symmetry, and WHAT it really is. Is it mirror particles that help explain gravity better? Do they stabilize reality? WHAT DO THEY DO AND WHAT ARE THEY!? Someone explain very simply, and neatly? Thanks.

tom.stoer
One idea was to unify ALL symmetries observed in nature, i.e. internal gauge symmetries and external spacetime (Poincare) symmetries. There is the general Coleman–Mandula no-go theorem saying that this is not possible.

But this no-go theorem has a loophole: it implicitly assumes that the conserved charges related to these symmetries are scalars. SUSY introduces spinorial charges - based on this new ingredient one can unify internal and spacetime symmetries. One can go one step further and gauge SUSY which results in SUGRA.

Okay....I think....

Then I still have this:

Can someone PLEASE explain the reason we factor in super symmetry, and WHAT it really is. Is it mirror particles that help explain gravity better? Do they stabilize reality? WHAT DO THEY DO AND WHAT ARE THEY!? Someone explain very simply, and neatly? Thanks.

tom.stoer
Up to now it does nothing b/c it's not there ... just kidding, SUSY particles haven't been identified so far; perhaps they show up at the LHC.

They would solve some problem in the standard model (and create some new ones); they would allow something like a better unification of three fundamental forces; they could explain dark matter; they could be an indication of supergravity and point towards a unification of all four forces.

I think the drawing above suggests an interpretation of SUSY as additional dimensions (one for each generator). You can find reference under the name superspace. This geometric formalism allows to simplify somewhat the calculations and their interpretation considerably. Those "dimensions" would be fermionic, that is qualitatively different from the ones we are used to : a particle could not move continuously in those direction. It could merely jump one step and no further, and this would turn its statistics from Bose-Einstein to Fermi-Dirac, or vice-versa. Alternatively, the world would be duplicated along those each of those dimensions, exhibiting a slightly distorted mirror image which tames the ultraviolet divergences.

haushofer
Okay....I think....

Then I still have this:

Can someone PLEASE explain the reason we factor in super symmetry, and WHAT it really is. Is it mirror particles that help explain gravity better? Do they stabilize reality? WHAT DO THEY DO AND WHAT ARE THEY!? Someone explain very simply, and neatly? Thanks.

In a lot of string theory texts it is often claimed that one "needs supersymmetry" to incorporate fermions in string theory, although I've never seen a clear argument for this. That's why SUSY is very attractive for string theory people. You could almost say: no SUSY, no superstringtheory, or string theory with fermions!

Another reason to believe SUSY makes sense is in the standard model itself. We know that the standard model predicts that at some energy scale all the three forces ALMOST can be combined (because the strength of the coupling constants become ALMOST the same). Since the standardmodel is not believed to be fundamental, people have no problems with the fact that this unification is ALMOST, but not exact.

SUSY improves this unification, which makes it for unification-loving physicists very attractive.

Another thing is that SUSY tempers the divergencies one encounters in doing calculations in the standard model. For that, look for "hierarchy problem", e.g. at wikipedia :)

fzero
Homework Helper
Gold Member
In a lot of string theory texts it is often claimed that one "needs supersymmetry" to incorporate fermions in string theory, although I've never seen a clear argument for this. That's why SUSY is very attractive for string theory people. You could almost say: no SUSY, no superstringtheory, or string theory with fermions!

The reasons behind this are the following. The lightest mode in the spectrum of the bosonic string is a tachyon, with $$m^2<0$$. Tachyons travel faster than light and therefore violate locality. They also signal an instability in the vacuum, since they behave as if they are at a local maximum of some potential.

Also, if we add any worldsheet fermions, then the spacetime theory will also have a massless spin 3/2 particle. Much like a massless spin 1 field always signals the presence of an unbroken local gauge symmetry, a massless spin 3/2 field signals the presence of unbroken local supersymmetry. If we try to couple such a field to a theory that is not locally supersymmetric, we will find negative-norm states, since much like for the gauge field, gauge-invariance is crucial to having a consistent quantum theory.

If we start with worldsheet supersymmetry, there is a projection onto physical states (the GSO projection) that both projects out the tachyon and ensures spacetime supersymmetry.

haushofer
The reasons behind this are the following. The lightest mode in the spectrum of the bosonic string is a tachyon, with $$m^2<0$$. Tachyons travel faster than light and therefore violate locality. They also signal an instability in the vacuum, since they behave as if they are at a local maximum of some potential.

Also, if we add any worldsheet fermions, then the spacetime theory will also have a massless spin 3/2 particle. Much like a massless spin 1 field always signals the presence of an unbroken local gauge symmetry, a massless spin 3/2 field signals the presence of unbroken local supersymmetry. If we try to couple such a field to a theory that is not locally supersymmetric, we will find negative-norm states, since much like for the gauge field, gauge-invariance is crucial to having a consistent quantum theory.

If we start with worldsheet supersymmetry, there is a projection onto physical states (the GSO projection) that both projects out the tachyon and ensures spacetime supersymmetry.

I know that with N=1 worldsheet SUSY and the GSO-projection you get what you want: spacetime SUSY and no tachyons. The question is: can a proper addition of fermions to the theory only be achieved via worldsheet SUSY? Have people investigated the possibility of incorporating fermions in the theory without SUSY (I'm sure they did), and what does it imply?

fzero
Homework Helper
Gold Member
I know that with N=1 worldsheet SUSY and the GSO-projection you get what you want: spacetime SUSY and no tachyons. The question is: can a proper addition of fermions to the theory only be achieved via worldsheet SUSY? Have people investigated the possibility of incorporating fermions in the theory without SUSY (I'm sure they did), and what does it imply?

As I said, you find a massless spin 3/2 field in the spectrum even without worldsheet SUSY. If you couple this field to other fields that don't preserve local spacetime SUSY (and these couplings are ubiquitous in the string perturbation theory), you will not be able to eliminate the longitudinal degree of freedom (which I believe to be a ghost by analogy with the massless vector field). The spacetime theory you get is therefore pathological and inconsistent.

haushofer
I'm sorry, now I'm reading your post again it seems like I simply overlooked that part! That makes a lot of sense, indeed.

Supersymmetry relates particles with different spins -- a supersymmetry operator turns a particle into one with a different spin.

In fact, some theorists once tried to construct some supersymmetric GUT that includes the entire Standard Model in a supersymmetry multiplet. However, they failed, and SUSY advocates now have more limited goals.

For instance, the Minimal Supersymmetric Standard Model has the best gauge unification of the various extensions of the Standard Model that have been investigated, and, of course, the Standard Model itself. In it, the three gauge coupling constants get very close at an energy of a few times 1016 GeV.

The MSSM also has various other predictions, including mass unification for
tau-bottom
gauginos
squarks and sleptons

at GUT energies. But the most reasonable mass ranges are around a few hundred GeV, enough to test with the LHC. So there's a lot to look forward to over the next few years.

Particles and their SUSY partners:
Higgs particles (0), higgsinos (1/2)
gauge particles (1), gauginos (1/2)
elementary fermions: quarks and leptons (1/2), sfermions: squarks and sleptons (0)
graviton (2), gravitino (3/2)

Despite repeated claims, string theory does not predict supersymmetry in our universe. In fact, one can have supersymmetry on the worldsheet without insisting on having it in the target space. It is usually called misaligned supersymmetry and was put forward AFAIK by Dienes in 94. We still hear about it now and then.

Supersymmetry versus gauge symmetry on the heterotic landscape

It is for me a reminder of claims that [thread=468837]string theory cannot break Lorentz invariance.[/thread]

fzero
Homework Helper
Gold Member
Despite repeated claims, string theory does not predict supersymmetry in our universe. In fact, one can have supersymmetry on the worldsheet without insisting on having it in the target space. It is usually called misaligned supersymmetry and was put forward AFAIK by Dienes in 94. We still hear about it now and then.

Supersymmetry versus gauge symmetry on the heterotic landscape

There is an additional constraint that doesn't seem to be addressed by Dienes. That is, if there is a massless spin 3/2 field in the spectrum, the target space theory must be locally supersymmetric. This is probably explained in the Weinberg-Witten paper, but the important detail is that there is at least one negative norm state that is pure gauge if local supersymmetry is present. If you couple the spin 3/2 particle to nonsupersymmetric matter, then there is no way to get rid of this ghost.

Dienes seems to be talking about theories with compact dimensions, so it is possible that there are no massless spin 3/2 fields in the low energy theory.

It is for me a reminder of claims that [thread=468837]string theory cannot break Lorentz invariance.[/thread]

I thought it was explained in that thread that string theory is Lorentz invariant at the level of the action and interactions, but that there can be backgrounds which are not themselves Lorentz invariant. This is just spontaneous symmetry breaking and in fact happens in general relativity on a specified curved manifold.

Indeed there has been always confusion about susy and string theory, partly based on sloppy or plainly incorrect statements. So let me make a few firm statements:

1) requirement of space-time fermions requires world sheet susy

2) world-sheet susy is a necessary but not sufficient condition for space-time susy;
world-sheet susy is a necessary but not sufficient condition for the absence of tachyons

(example: there are ten dimensional heterotic strings other than the ones usually mentioned, they are not supersymmetric, and only the one with O(16)xO(16) gauge symmetry has no tachyon at tree level).

-> statements that string theory predicts space-time susy are false, no matter how popular the one who claims it

What is implicitly meant is that the only theories that are "known" to be consistent/stable, are supersymmetric. But that nature must be actually supersymmetric (down to some scale, then broken), cannot be concluded from that. I see it as a technical assumption for having tractable toy models, however others believe literally in this. It is a bit like confusing N=4 susy gauge theory, which is highly tractable and therefore receives a lot of attention, with real-world QCD.