Vacua, walls and junctions in GNF,NC

Abstract

We discuss vacua, walls and three-pronged junctions of the mass-deformed nonlinear sigma models on the Grassmann manifold, which are non-Abelian gauge theories for N C ≥ 2. Polyhedra are proposed in [1] to describe Bogomol'nyi-Prasad-Sommerfield objects of the mass-deformed nonlinear sigma models on the complex projective space, which are Abelian gauge theories. We show that we can produce similar polyhedra for the mass-deformed nonlinear sigma models on the Grassmann manifold by applying the moduli matrix formalism [2] and the pictorial representation [3]. Non-Abelian junctions can be analysed by making use of the polyhedra instead of the Plücker embedding. We present diagrams for vacua, walls and three-pronged junctions, and compute three-pronged junction positions of the mass-deformed nonlinear sigma models on the Grassmann manifold. We show that the results are consistent with the known results of [4], which are worked out by using the Plücker embedding. *

Junctions of mass-deformed nonlinear sigma models on $SO(2N)/U(N)$ and $Sp(N)/U(N)$ II

“…Junctions of mass-deformed nonlinear sigma models on the complex projective space and on the Grassmann manifold are studied in the moduli matrix formalism [16,17,18]. In [17], three-pronged junctions of the mass-deformed nonlinear sigma model on the Grassmann manifold are constructed by embedding the Grassmann manifold to the complex projective space using the Plücker embedding.…”

“…In [17], three-pronged junctions of the mass-deformed nonlinear sigma model on the Grassmann manifold are constructed by embedding the Grassmann manifold to the complex projective space using the Plücker embedding. In [18], three-pronged junctions of the mass-deformed nonlinear sigma models on the Grassmann manifold are constructed by utilising diagrams of the pictorial representation, which is proposed in [14]. In [19], three-pronged junctions of the mass-deformed nonlinear sigma models on SO(8)/U (4) and Sp(3)/U (3) are constructed by the diagram method, which is proposed in [18].…”

Exact solutions of domain wall junctions in arbitrary dimensions

“…They are called the 1 4 BPS states and are accompanied with a junction topological charge Y in addition to Z m (m ¼ 1, 2). 1 The 1 4 BPS domain wall junctions have been also studied in N ¼ 1 SUSY models [33,[71][72][73][74][75][76][77][78][79] and N ¼ 2 SUSY models [80][81][82][83][84][85][86][87][88][89]. The domain wall junctions are similar to vortex strings, but the junction charge Y was found to negatively contribute to the total energy [73][74][75] in contrast to the domain wall charge Z 1;2 always contributing positively to the total energy.…”

Junctions of mass-deformed nonlinear sigma models on SO(2N)/U(N) and Sp(N)/U(N). Part II

“…Junctions of mass-deformed nonlinear sigma models on the complex projective space and on the Grassmann manifold are studied in the moduli matrix formalism [25][26][27][28]. In [25], three-pronged junctions of mass-deformed nonlinear sigma models on the complex projective space are studied.…”

“…In [26], three-pronged junctions of mass-deformed nonlinear sigma models on the Grassmann manifold are constructed by embedding the Grassmann manifold to the complex projective space using the Plücker embedding. In [27,28], three-pronged junctions of mass-deformed nonlinear sigma models on the Grassmann manifold are constructed by reformulating diagrams for vacua and walls in the pictorial representation that is proposed in [23]. This method produces diagrams, which are similar to the polyhedron diagrams of [25].…”