Can we have exact supersymmetry with undetected superpartners? Lessons from 2+1 dimensions

We show that the exact solution of the two-superbody problem in N = 2 Chern Simons supergravity in 2+1 dimensions leads to a supermultiplet of space-times. This space-time supermultiplet can be described in terms of an ''operator line element'' which acts on the Hilbert space of Poincare states which make up the equivalent one-superbody source. For large distance physics, the corresponding geometry may be viewed as that of a spinning cone with an additional finite discrete dimension. One of the interesting features of this universe is that superpartners of a given particle lie in different components of this supersymmetric space-time. Therefore, to have any hope of detecting the superpartners of known particles, supersymmetry must remain exact.