  A few exact results concerning topological currents in field theories are
obtained. It is generally shown that, a topological charge can not generate any
kind of symmetry transformation on the fields. It is also proven that, the
existence of a charge that does not generate any kind of symmetry
transformation on the fields, has to be of topological origin. As a
consequence, it is found that in a given theory, superconductivity via
Anderson-Higgs route can only occur if the gauge coupling with other fields is
minimal. Several physical implications of these results are studied.
