Localization of Non-Abelian Gauge Fields on Domain Walls at Weak Coupling (D-brane Prototypes)

TL;DR

This work develops a field-theoretic D-brane prototype by studying ${\cal N}=2$ SQCD with gauge group ${\rm SU}(2)\times {\rm U}(1)$ and $N_f=4$, in a weakly coupled quark-vacuum regime. By constructing elementary and composite domain walls, it demonstrates that while a single wall localizes only an Abelian gauge field, a bound composite wall supports a non-Abelian gauge field on its $(2+1)$-D worldvolume; this is accompanied by a 1/4-BPS non-Abelian string ending on the wall, whose endpoint acts as a non-Abelian charge in the wall theory. The analysis develops the central charges, Bogomolny equations, and the effective wall theories, revealing a bulk/brane-like duality in which wall dynamics and non-perturbative effects mimic D-brane intuition. The results illuminate how domain walls and flux tubes can realize non-Abelian gauge dynamics in lower dimensions and establish a concrete link between 3+1D SUSY gauge theories and D-brane-inspired worldvolume physics with potential implications for confinement and duality structures. Overall, the paper expands the dictionary between brane pictures and field theory, showing practical mechanisms for non-Abelian localization and gauge-field realization on domain-wall defects.

Abstract

Building on our previous results, we study D-brane/string prototypes in weakly coupled (3+1)-dimensional supersymmetric field theory engineered to support (2+1)-dimensional domain walls, "non-Abelian" strings and various junctions. Our main but not exclusive task is the study of localization of non-Abelian gauge fields on the walls. The model we work with is N=2 QCD, with the gauge group SU(2)x$U(1) and N_f=4 flavors of fundamental hypermultiplets (referred to as quarks), perturbed by the Fayet-Iliopoulos term of the U(1) factor. In the limit of large but almost equal quark mass terms a set of vacua exists in which this theory is at weak coupling. We focus on these vacua (called the quark vacua). We study elementary BPS domain walls interpolating between selected quark vacua, as well as their bound state, a composite wall. The composite wall is demonstrated to localize a non-Abelian gauge field on its world sheet. Next, we turn to the analysis of recently proposed "non-Abelian" strings (flux tubes) which carry orientational moduli corresponding to rotations of the "color-magnetic" flux direction inside a global O(3). We find a 1/4-BPS solution for the string ending on the composite domain wall. The end point of this string is shown to play the role of a non-Abelian (dual) charge in the effective world volume theory of non-Abelian (2+1)-dimensional vector fields confined to the wall.

Figures (10)

• Figure 1: The scale hierarchy: illustrating the fact that the gauge couplings never become large in the problem at hand. According to Eq. (\ref{['defxi']}) $\mu\, m =\xi/6$.
• Figure 2: Two elementary walls which comprise a composite $12\to 34$ wall.
• Figure 3: The vacuum structure on the $(I\,,\,\, I_3)$ plane.
• Figure 4: Internal structure of the $12\to 14$ 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 5: Root and weight vectors of the SU(3) algebra.