My current research interest is cybersusy, which is a method that gives rise to a new mechanism for supersymmetry breaking in the standard model.
Cybersusy has some very nice features. In the first place it arises from the supersymmetric standard model. It just has not been noticed before, because it is very well hidden in the cohomology of the theory, which is hard to compute. It gives rise to a scheme of supersymmetry breaking which is proportional to gauge symmetry breaking. The vacuum energy remains zero after supersymmetry breaking, and there are no mass sum rules. The application of this to the leptons in the standard supersymmetric model is consistent with the presently known spectrum of leptons--in other words all the superpartners of the leptons can be made much heavier than the electron, muon and tau, and similarly for the neutrinos.
The reason these are nice features is that other supersymmetry breaking mechanisms suffer problems that are cured by cybersusy.
The most popular method currently is to simply start with the standard supersymmetric model and then break supersymmetry explicitly by adding mass terms that break supersymmetry `softly'. The trouble with this is that there is no known theoretical reason to do this. We do it because if we do not do it, the theory does not agree with experiment. Also it flies in the face of the reason for looking at supersymmetry in the first place, because the action one uses is simply not supersymmetric once the new terms are added.
Another method, which was originally considered promising, many years ago, was the method of introducing spontaneous breaking of supersymmetry by choosing the superpotential in some clever way. The problem here is that before spontaneous breaking of supersymmetry the vacuum energy is zero, and after spontaneous breaking of supersymmetry the vacuum energy is ridiculously huge, which would give rise to a ridiculously huge cosmological constant. Also, spontaneous breaking tends to be inconsistent with experiment anyway, because some of the superpartners get masses that are too small, as a result of mass sum rules.
Cybersusy arises from the construction of an effective action. This action is motivated by the BRS cohomology for supersymmetry applied to the standard supersymmetric model.
One of the most interesting features of the BRS cohomology of the Wess Zumino model is that there is a constraint equation which must be satisfied in order that certain composite dot-spinor operators transform as effective superfields.
Solutions of these constraints in general seem hard to find. However the supersymmetric standard model provides nice solutions to these constraints, and these solutions are familiar particles such as the supersymmetric generalization of the baryons constructed from three quarks.
The existence of these solutions depends on some of the weird features of the standard model, in particular it depends on the left right assymetry of the quark and lepton content of the standard model, on the three generations, on the direct product structure of the gauge groups SU(3) X SU(2) X U(1), and also on the spontaneous breaking of gauge symmetry. So it appears as though the standard model is `rigged' to provide nice solutions to the constraint equations, and in turn this is the origin of supersymmetry breaking. This is discussed in Cybersusy V in a fairly general way.
The essentials are set out in Cybersusy I which is Supersymmetry Breaks when Gauge Symmetry Breaks: Cybersusy I .
This is retrievable using arXiv:0808.0811 [ps, pdf, other].
Then there are four other papers that follow: Cybersusy II,III,IV and V. They can be found below:
arXiv:0808.3749 [ps, pdf, other]
iv:0808.2301 [ps, pdf, other]
iv:0808.2276 [ps, pdf, other]
arXiv:0808.2263 [ps, pdf, other]
Many of my earlier papers on supersymmetry and anomalies were a search for anomalies that corresponded to the cohomology of supersymmetry that was set out in two papers published in 1995 in Communications in Mathematical Physics. Those two papers are correct. However many of the papers after that contained new results and also speculation about the existence of supersymmetry anomalies. The speculations, I now believe, are largely wrong. The anomalies do not exist--they appear as mass dependent cybersusy algebra modifications. These are similar algebraically to anomalies, but they act quite differently.
The history of these errors, and my current view of the correct situation, are set out in the first cybersusy paper (I above).
