Localization of non-Abelian gauge fields on domain walls at weak coupling: D-brane prototypes

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.