A. V. Yung

 

Bulk-brane duality in field theory

 

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 ($W\bar W$) on a {\sl cylinder}. We argue that for certain values of parameters this set-up provides an example of a controllable analog of 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 \ntwo 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 {\sl 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.