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

TL;DR

The paper constructs a controlled field-theoretic realization of D-brane/string concepts within ${\cal N}=2$ SQCD by studying (2+1)-D domain walls in a (3+1)-D SU(2) theory with two quark flavors and a small adjoint-mass perturbation. It shows that the domain wall localizes a massless ${U(1)}$ gauge field and that an ANO flux tube can end on the wall, yielding a 1/4-BPS wall–string junction with the end-point acting as a charge in the wall’s 2+1D dual theory, effectively reproducing a D-brane–string picture in a calculable regime. The wall carries two moduli ($z_0$ and $\sigma$) with a two-component 2+1D ${\cal N}=2$ worldvolume theory; the effective coupling on the wall is $e_{2+1}^2=4\pi^2\,\frac{\xi}{\Delta m}$, and the low-energy dynamics persist under softly broken ${\rm N}=2 \to 1$ as long as higher-derivative effects are small. The work also discusses the strong-coupling monopole–dyon wall puzzle (the “missing wall”) and suggests a resolution via wall moduli dynamics, linking to broader brane-inspired results (e.g., Acharya–Vafa), with implications for potential non-Abelian wall physics in future studies.

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.

Figures (5)

• Figure 1: Geometry of the wall-string junction. The gauge field localized on the wall can be cast in the form of a dual 1+2 dimensional electrodynamics. This field is dual to the gauge field higgsed in the bulk. The probe magnetic charge in the bulk (the magnetic monopole of the original ${\cal N}=2\;$ SQCD) is denoted by asterisk.
• Figure 2: A schematic rendition of the domain wall in the model (\ref{['syfone']}).
• Figure 3: Internal structure of the domain wall: two edges (domains $E_{1,2}$) of the width $\sim \xi^{-1/2}$ are separated by a broad middle band (domain $M$) of the width $R$, see Eq. (\ref{['R']}).
• Figure 4: The translational zero mode.
• Figure 5: Bending of the wall due to the string-wall junction. The flux tube extends to the right infinity. The wall profile is logarithmic at transverse distances larger than $\xi^{-1/2}$ from the string axis. At smaller distances the adiabatic approximation fails.