Domain walls and flux tubes inN=2SQCD: D-brane prototypes

Abstract

This paper could have been entitled ``D branes and strings from flesh and blood.'' We study field theoretic prototypes of D branes or strings. To this end we consider (2+1)-dimensional domain walls in (3+1)-dimensional $\mathcal{N}=2$ supersymmetric QCD with an SU(2) gauge group and ${N}_{f}=2$ 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 $\mathcal{N}=2$ supersymmetry, and reduces to a (generalized) Fayet-Iliopoulos term in the effective low-energy $\mathcal{N}=2$ supersymmetric QED (SQED). We find a 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 or string picture we consider the Abrikosov-Nielsen-Olesen 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 $\mathcal{N}=1$ theory is discussed. Our results lead us to a conjecture regarding the notorious ``missing wall'' in the solution of Kaplunovsky, Sonnenschein, and Yankielowicz.