  We consider (3+1)-dimensional N=2 supersymmetric QED with two flavors of
fundamental hypermultiplets. This theory supports 1/2-BPS domain walls and flux
tubes (strings), as well as their 1/4-BPS junctions. The effective
(2+1)-dimensional theory on the domain wall is known to be a U(1) gauge theory.
Previously, the wall-string junctions were shown to play the role of massive
charges in this theory. However, the field theory of the junctions on the wall
(for semi-infinite strings) appears to be inconsistent due to infrared
problems. All these problems can be eliminated by compactifying one spatial
dimension orthogonal to the wall and considering a wall-antiwall system on a
cylinder. We argue that for certain values of parameters this set-up provides
an example of a controllable bulk-brane duality in field theory. Dynamics of
the 4D bulk are mapped onto 3D boundary theory: 3D N=2 SQED with two matter
superfields and a weak-strong coupling constant relation in 4D and 3D,
respectively. The cylinder radius is seen as a "real mass" in 3D N=2 SQED. We
work out (at weak coupling) the quantum version of the world-volume theory on
the walls. Integrating out massive matter (strings in the bulk theory) one
generates a Chern-Simons term on the wall world volume and an interaction
between the wall and antiwall that scales as a power of distance. Vector and
scalar (classically) massless excitations on the walls develop a mass gap at
the quantum level; the long-range interactions disappear. The above duality
implies that the wall and its antiwall partner (at strong coupling in the bulk
theory) are stabilized at the opposite sides of the cylinder.
