Partial supersymmetry and a model of unification

Within 4 dimensional local field theory an attempt of constructing a gauge theory consisting of left-handed supergravity (SUGRA) part and non-supersymmetric left-handed spin 1/2 matter part is performed. The gauge symmetry is inspired by a higher gauge symmetry which is based on a four dimensional spacetime specified by (xμ,θαμ (x)), where θαμ(x) is a vector-spinor. These may be regarded as the world space coordinate analogue of string theory. The research along this line may be worth pursuing from the viewpoints that SUSY, as a whole symmetry, may be so restrictive to realize in a complicated way the observed low energy chiral symmetry. (author)