Vacua, walls and junctions in G(NF), (NC)

Abstract

We discuss vacua, walls and three-pronged junctions of the mass-deformed nonlinear sigma models on SU) the Grassmann manifold G(NF), (NC )= SU(N-F)/SU(N-C) x SU(N-F-N-C)xU (1), 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 Plucker 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 Plucker embedding. (C) 2019 The Author. Published by Elsevier B.V.