  There exists a formulation of the Maxwell theory in terms of two vector
potentials, one electric and one magnetic. The action is then manifestly
invariant under electric-magnetic duality transformations, which are rotations
in the two-dimensional internal space of the two potentials, and local. We ask
the question: can duality be gauged? The only known and battled-tested method
of accomplishing the gauging is the Noether procedure. In its decanted form, it
amounts to turn on the coupling by deforming the abelian gauge group of the
free theory, out of whose curvatures the action is built, into a non-abelian
group which becomes the gauge group of the resulting theory. In this article,
we show that the method cannot be successfully implemented for
electric-magnetic duality. We thus conclude that, unless a radically new idea
is introduced, electric-magnetic duality cannot be gauged. The implication of
this result for supergravity is briefly discussed.
