Domain Walls and Flux Tubes in N = 2 SQCD: D-Brane Prototypes

This paper could have been entitled “D branes and strings from flesh and blood.” We study field theoretic prototypes of D branes/strings. To this end we consider (2+1)-dimensional domain walls in (3+1)-dimensional N = 2 SQCD with SU(2) gauge group and Nf = 2 flavors of fundamental hypermultiplets (quarks). This theory is perturbed by a small mass term of the adjoint matter which, in the leading order in the mass parameter, does not break N = 2 supersymmetry, and reduces to a (generalized) Fayet-Iliopoulos term in the effective low-energy N = 2 SQED. We find 1/2 BPS-saturated domain wall solution interpolating between two quark vacua at weak coupling, and show that this domain wall localizes a U(1) gauge field. To make contact with the brane/string picture we consider the Abrikosov-NielsenOlesen magnetic flux tube in one of two quark vacua and demonstrate that it can end on the domain wall. We find an explicit 1/4 BPS-saturated solution for the wall/flux tube junction. We verify that the end point of the flux tube on the wall plays the role of an electric charge in the dual 2+1 dimensional SQED living on the wall. Flow to N = 1 theory is discussed. Our results lead us to a conjecture regarding the notorious “missing wall” in the solution of Kaplunovsky et al.