Webs of domain walls in supersymmetric gauge theories

Abstract

Webs of domain walls are constructed as 1/4 BPS states in d = 4, N = 2 supersymmetric U (N C ) gauge theories with N F hypermultiplets in the fundamental representation. Web of walls can contain any numbers of external legs and loops like (p, q) string/5-brane webs. We find the moduli space M of a 1/4 BPS equation for wall webs to be the complex Grassmann manifold. When moduli spaces of 1/2 BPS states (parallel walls) and the vacua are removed from M, the non-compact moduli space of genuine 1/4 BPS wall webs is obtained. All the solutions are obtained explicitly and exactly in the strong gauge coupling limit. In the case of Abelian gauge theory, we work out the correspondence between configurations of wall web and the moduli space CP N

Junctions of mass-deformed nonlinear sigma models on the Grassmann manifold

“…We use the index α = 1, 2 for codimensions and adjoint scalars as it is done in [17]. The energy density (2.14) and the tension density (2.15) are constrained by (2.9).…”

“…4 Three-pronged junctions A three-pronged junction is formed by three vacua interpolated by three non-penetrable walls. A wall that interpolates vacuum A and vacuum B has a tension T AB pulling the junction along the wall direction outwards [17] T AB = (−Z AB 2 , Z AB 1 ),…”

“…The diagram of G N F +1,N C repeats the diagram of G N F ,N C . It is also shown in [20] that by reformulating the diagrams in the pictorial representations, we can produce polyhedra, which are similar to the polyhedra that are introduced to study BPS objects of the mass-deformed nonlinear sigma models on the complex projective space [17]. Vertices, edges and triangular faces correspond to vacua, walls and three-pronged junctions.…”

“…A three-pronged junction is formed by a set of three vacua that are interpolated by walls. Three-pronged junction solutions are discussed in the moduli matrix formalism [17,18,19]. The moduli matrix formalism can be easily applied to Abelian junctions, but it becomes complicated with non-Abelian junctions.…”

Walls of massive Kähler sigma models onSO(2N)/U(N)andSpArai1, Shin2 2011Phys. Rev. D160310View full textAdd to dashboardCite

“…This construction method is called the moduli matrix approach. Subsequently, this approach has been applied to obtain other types of solitonic solutions such as monopole-vortex-wall systems [8], domain wall webs [9], non-Abelian vortices [10], instanton-vortex systems [11], and Skyrmions [12]. For a comprehensive review, see [13].…”