Geometrical approach to local gauge and supergauge invariance: Local gauge theories and supersymmetric strings

A geometrical analysis of local gauge invariance is presented. By extending the four directions in space-time which can define a light cone to an enlarged tangent space, we construct a superspace in which the intimate relationship between purely kinematic invariances and those of local internal symmetry groups are explored. Three applications are considered: (1) Local gauge theories in flat or curved space-time are derived from a scalar action in superspace. As a result, the theory has an extra dimensional parameter. (2) Born-Infeld electrodynamics and its non-Abelian counterpart are extended to curved space-time. This suggests a new set of gravitational field equations. (3) The formalism is extended to the case in which the connection forms anticommute and supersymmetric string models are constructed, which give action-principle formulations of the known dual models involving fermions and suggest possibilities for constructing new models. Applications to gravitation and local supersymmetry are pointed out.