Abstract
We discuss vacua, walls and three-pronged junctions of the mass-deformed nonlinear sigma models on the Grassmann manifold GNF,NC=SU(NF)SU(NC)×SU(NF−NC)×U(1), which are non-Abelian gauge theories for NC≥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.
Highlights
The moduli matrix formalism is proposed to construct 1/2 Bogomol’nyi-Prasad-Sommerfield (BPS) walls in non-Abelian gauge theories [2]
The moduli spaces are described by pictorial representations in which the vacua and the elementary walls correspond to vertices and line segments in the representation [3]
We show that we can produce polyhedra, which are similar to the polyhedra [1] that are introduced to study BPS objects of the mass-deformed nonlinear sigma models on the complex projective space, by reformulating diagrams for vacua and elementary walls in the pictorial representation
Summary
The moduli matrix formalism is proposed to construct 1/2 Bogomol’nyi-Prasad-Sommerfield (BPS) walls in non-Abelian gauge theories [2]. Three-pronged junctions of the mass-deformed nonlinear sigma models on GNF ,NC , which are non-Abelian gauge theories for NC ≥ 2, are studied in [4]. In [4], the Grassmann manifold GNF ,NC is embedded into the complex projective space CP NF CNC −1 by the Plucker embedding resolving the complications This method cannot be directly applied to junctions of the mass-deformed nonlinear sigma models on SO(2N )/U (N ). We show that we can produce polyhedra, which are similar to the polyhedra [1] that are introduced to study BPS objects of the mass-deformed nonlinear sigma models on the complex projective space, by reformulating diagrams for vacua and elementary walls in the pictorial representation.
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