  We study the dynamical localization of a massless gauge field on a
lower-dimensional surface (2-brane). In flat space, the necessary and
sufficient condition for this phenomenon is the existence of confinement in the
bulk. The resulting configuration is equivalent to a dual Josephson junction.
This duality leads to an interesting puzzle, as it implies that a localized
massless theory, even in the Abelian case, must become confining at
exponentially large distances. Through the use of topological arguments we
clarify the physics behind this large-distance confinement and identify the
instantons of the brane world-volume theory that are responsible for its
appearance. We show that they correspond to the (condensed) bulk magnetic
charges (monopoles), that occasionally tunnel through the brane and induce weak
confinement of the brane theory. We consider the possible generalization of
this effect to higher dimensions and discuss phenomenological bounds on the
confinement of electric charges at exponentially large distances within our
Universe.
