What is the geometric interpretation of supersymmetry?

I recently had the opportunity to attend lectures on mathematical physics by Cumrun Vafa and Edward Witten, and one idea that they both alluded to explains supersymmetry in terms of a geometric formulation of the standard model. I guess the idea is that the electromagnetic, weak, and strong fields are realized in quantum field theory as principal U(1), SU(2), and SU(3) bundles respectively, so that the standard model has structure group (gauge group) U(1)xSU(1)xSU(3). I am also acquainted with the notion that Maxwell's equations can be formulated in this context as the Bianchi identity for the curvature of a certain connection on the principal U(1) bundle in question, and I gather that one can obtain similar results in this fashion for the weak and strong nuclear forces. The idea that Vafa and Witten both kind of mentioned in passing is that to properly choose a connection on the principal U(1)xSU(2)xSU(3) bundle in such a way that matches physical observation one must take energy as a free parameter and that supersymmetry is the statement that something geometrically special happens at a certain (high) energy level. Does anybody know the full story, or at least have some references? I am coming at this from a mathematical background, and I have a lot of trouble with physics language (for example, I have no idea what a particle actually is, let alone fermions or bosons). I also posted this question in the physics area. Thanks!