Symmetry in describing theories of physics (the standard model) refers to the fact that most equations do not have to be changed if certain types of transformations are made. Some symmetries refer to spatial symmetry - if you rotate your experiment for example, you don't have to derive new equations for motion. Other types of symmetry apply to interactions involving particles - if you interchange particles in some equations, they still apply - and since all particles are different from each other in some manner, those are rather unique.

Supersymmetry (or SUSY) is a hypothetical expansion of the standard model involving a a type of symmetry of the particle kind. There are essentially two types of particles - those with matter (proton, quark, lepton - all fermions, all with spin of 1/2 unit) and those with force (photon, gluon - all bosons, all with integer spin), and the two types have different sets of equations that describe them. Supersymmetry suggests that these equations do not change if you replace force particles with matter particles and vice-versa - this is rather remarkable, considering how different the observed types of each particle are. Essentially, it creates a clear connection between the two distinct types of particles.

If this theory is true, each particle would need a "superpartner", a particle of the other type that can be plugged into the equations. However, it was quickly obvious that no existing particles can be partners of each other. Thus, for each force particle, there must be a matter particle, and vice versa. A simple method of naming has been created to talk about these particles. Each matter particle was given a partner with the same name and a "s-" prefix, so quarks have squarks, leptons have sleptons, electrons have selectrons. Force particles were given partners with their suffix changed to "-ino", so photons have photinos, gluons have gluinos. It also turns out that supersymmetry is a "broken" symmetry - the superparticles would be much more massive than all known elementary particles, or they would have been seen already. (How much more? Predictions of the particle masses put them in the 100-1000 GeV range - or 100 to 1000 times more massive than a proton)

Supersymmetry is also necessary for superstring theory to possibly be correct, and will help considerably toward moving to a Grand Unified Theory.

So far, no evidence has been found to support this theory. Because of the increased mass, much higher energies are needed in particle colliders to create them. However, there are a number of interesting consequences should this theory be true. For example, the Higgs boson part of the standard model doesn't really fit into the rest of the model, and a lot of assumptions have to be made. Syupersymmetry, however, lets many of the properties of the Higgs bosons be mathematically derived. Also, the "dark matter" commonly talked about that must be scattered aroung the universe has no real explanation in the standard model. Supersymmetry also predicts the existance of this matter, and gives a candidate for the particle that makes up this matter. (a higgsino, the superpartner to the Higgs boson)

There have been hints as to the existance of superparticles in some experiments. CDF collaboration at Fermilab sometime in 1995-96 reported an event that can be interpreted as the production of a selectron and its antiparticle, followed by the decay of the selectron to a photino and an electron, and then the decay of the photino to a photon and a higgsino. That such a decay chain might be the way superpartners were detected was predicted in about 1986 - it was not invented after the event was found). The expected production rate for Fermilab suggests that about one event should be found in the two years of data they have recently accumulated.

One of the big hopes for the Superconducting Supercollider project that was being worked on in the United States was that it would help prove/disprove this theory. With energies that would have been around 20,000 GeV per beam, that would have been plenty to create and observe superparticles. Instead, hopes are the large hadron collider (LHC) at CERN in Geneva, Switzerland will possibly produce them, at about 8,000 GeV per beam.

Sources:
APR Virtual Pressroom May 96 - Lay Language Papers, Supersymmetry--What Is it?--Status?--Why So Important?, http://www.aps.org/april96/vpr/B12.01.html
Supersymmetry, http://www.theory.caltech.edu/people/jhs/strings/string12.html

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