SL(2,C)-gauge theory andN=1 supergravity

It is shown that as Riemannian space may be taken to give rise to a Poincaré gauge theory of gravitation, the superspace where the coordinates are given by (X, ), being a spinorial variable gives rise to anSL(2, C)-gauge theory and corresponds toN= 1 supergravity. It leads to a conserved current and the conserved quantity here corresponds to isospin, where the latter is taken to be generated from conformal reflection. Thus, supergravity plays a predominant role in the microlocal space-time.