Superunified theories based on the geometry of local (super-) gauge invariance

Abstract

Based on the geometry of local (super-) gauge invariance, a theoretical framework for constructing superunified theories is given. The main ingredients of this approach are (a) a method of constructing invariants associated with unconstrained gauge theories and (b) the concept of "constrained" geometries for the description of gravity and supergravity as well as the choice of their gauge groups. It is argued that any unified theory must contain gravity, and then, to retain the invariances of pure gravity theory, such a theory must be a superunified one. The formalism is then applied, respectively, to pure gravity, gravity coupled to Yang-Mills fields, simple supergravity, and SO(2)-extended supergravity. Important properties of these theories are discussed in detail.