  We provide a mechanism of gauging a theory based on a particular way to embed
a theory on a target space such that a nontrivial fibration is produced. A
connection over a nontrivial fibration with monodromy provides a natural
framework for a new way of gauging a theory. Moreover, properties of the global
symmetry of the original theory are included in a particular way in the new
theory. This mechanism for gauging a symmetry preserves the total number of
degrees of freedom in distinction with the classical one. We consider a
particular example to illustrate the mechanism: by reinterpreting the
supermembrane with central charges as a gauged supermembrane of the
compactified supermembrane according to this new sense of gauging. Further
applications are also discussed.
