The Structure of Space-Time Emerging from the Two-Superbody Problem in Chern Simons Supergravity

Abstract

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 supersymmetric space-time is characterized by the two gauge invariant observables of the super Poincare' group, which may be viewed as the Casimir invariants of an equivalent one-superbody state. The metric of this space-time supermultiplet can be cast into the form of the metric for a spinning cone in which the coordinates do not commute or for a spinning cone with an additional finite discrete dimension. Some of the interesting features of this universe and their possible physical implications are discussed in the light of a corresponding observation by Witten.