Nonlinear gauge fields and the structure of gravity and supergravity theories

By regarding the gauge fields which arise in theories based on nonlinear realizations of gauge symmetries as dynamical variables, we show that gravity, with or without matter, supergravity, and extended supergravity theories possess such symmetries. The model-independent transformation laws for such fields remain unaltered when extended supergravity theories are considered. For groups such as $\mathrm{OSp}(N; 4)$, the supersymmetry part of the group must be realized nonlinearly. It is pointed out that in this scheme to realize supersymmetry transformations linearly, one possibility is to consider the inhomogeneous extensions of the supergroups $\mathrm{OSp}(N; 2C)$, i.e., $\mathrm{IOSp}(N; 2C)$. We also consider the consequences of this point of view in regard to flat-space-time gauge theories and show that instead of the usual set of Yang-Mills equations supplemented with gauge conditions which break the gauge covariance completely, it is possible to formulate a system of equations which are equal in number to the above set but which maintain gauge covariance with respect to the unbroken part of the gauge symmetry.