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

TL;DR

This paper constructs and analyzes supersymmetric domain walls and flux tubes in N=2 SQCD, demonstrating their interactions and dualities, and providing field theoretic prototypes of D-branes and strings.

Contribution

It presents explicit BPS solutions for domain walls and flux tubes in N=2 SQCD, illustrating their brane/string analogies and the localization of gauge fields on walls.

Findings

Domain walls interpolate between quark vacua at weak coupling.

Flux tubes can end on domain walls, forming junctions.

End points of flux tubes act as electric charges on the wall's SQED.

Abstract

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 two quark flavors in the fundamental representation. 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-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 N=1 theory is discussed. Our results lead us to a conjecture regarding the notorious "missing wall" in the solution of Kaplunovsky et al.