Vacua and walls of mass-deformed Kähler nonlinear sigma models on Sp(N)/U(N)

Abstract

We study vacua and walls of mass-deformed Kähler nonlinear sigma models on Sp(N )/U (N ). We identify elementary walls with the simple roots of U Sp(2N ) and discuss compressed walls, penetrable walls and multiwalls by using the moduli matrix formalism.Kähler and hyper-Kähler nonlinear sigma models are studied in [1,2,3]. Massive hyper-Kähler nonlinear sigma models have a potential which is proportional to the square of a tri-holomorphic Killing vector field of the hyper-Kähler target space [4]. Fixed points of the Killing vector field are realized as discrete vacua. It was shown that there exist 1/2 supersymmetric kink solutions that interpolate the discrete vacua [5]. A more general potential is possible for a hyper-Kähler target space of quaternionic dimension two or more, and exact non-singular solutions representing intersecting domain walls are constructed in [6]. Multi-domain walls are studied in [7].The moduli matrix formalism [8,9] was proposed to construct walls systematically in non-Abelian gauge theories with N = 2 supersymmetry in four-dimensional spacetime. The model considered in [8,9] becomes massive hyper-Kähler nonlinear sigma models on the cotangent bundle over the Grassmann manifold T * G N F ,N C 1 when the gauge coupling is taken to be infinity. In this limit, multiwalls are constructed as well as single walls. Multiwalls are along one spatial direction and their positions depend on moduli parameters and mass parameters. Walls can be compressed to single walls by changing moduli parameters in Abelian gauge theories and in non-Abelian gauge theories. These walls are called compressed walls. A distinguishing feature in the non-Abelian gauge theories is that walls can pass through each other [9]. Such walls are called penetrable walls. It was also shown in [9] that there is a bundle structure for nondegenerate masses, so that the vacua and the walls are on the Kähler manifold.The walls of Kähler nonlinear sigma models on SO(2N )/U (N ) are studied in [10,11]. The Hermitian symmetric space SO(2N )/U (N ) is realized as a quadric in the Grassmann manifold G 2N,N in accordance with [12,13]. As SO(4)/U (2) CP 1 and SO(6)/U (3) CP 3 [14], the nonlinear sigma models on SO(2N )/U (N ) with N = 2 and N = 3 are actually Abelian gauge theories. The walls of the nonlinear sigma models on SO(2N )/U (N ) with N = 2, 3 are studied in [10]. The walls of the nonlinear sigma models on SO(2N )/U (N ) for any N are studied in [11]. Penetrable walls, which are related to non-Abelian nature, appear in N ≥ 4 cases. The vacua and the walls of N ≤ 7 cases are presented in pictorial representations where vacua and elementary walls correspond to the vertices and the segments of the representations. It is shown that there is a recurrence of a two dimensional diagram for each N mod 4 in the vacuum structures that are connected to the maximum number of elementary walls. The vacuum structures are proved by induction.The purpose of this paper is to construct walls of mass-deformed Kähler nonlinear sigmaSU (N C )×SU (N F −N C...

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

“…The moduli matrix formalism can be applied to the mass-deformed nonlinear sigma models on the quadrics as it is done in [13,14]. Three-pronged junctions of the mass-deformed nonlinear sigma models on SO(8)/U(4) and Sp(3)/U(3) are constructed by reformulating the diagrams for vacua and walls that are obtained in [23,24].…”

“…In this paper, we construct three-pronged junctions of mass-deformed nonlinear sigma models on SO(2N )/U(N ) and Sp(N )/U(N ) for generic N by using the moduli matrix formalism [13,14] and the pictorial representation [23,24]. The nonlinear sigma models on the quadrics that have junction solutions are obtained by complexifying the mass matrix and the adjoint scalar field of the N = 1 nonlinear sigma models on the quadrics.…”

“…Vacua and walls of mass-deformed nonlinear sigma models on SO(2N )/U(N ) and Sp(N )/U(N ) are constructed in the N = 1 supersymmetric nonlinear sigma models [21,23,24]. The bosonic part of the Lagrangian is…”

“…Hermitian symmetric spaces SO(2N )/U(N ) and Sp(N )/U(N ) are quadrics of the Grassmann manifold [16][17][18][19][20]. Kink solutions are studied on SO(2N )/U(N ) and Sp(N )/U(N ) [21][22][23][24].…”

Exact solutions of domain wall junctions in arbitrary dimensions

“…Their topological charges are directly connected to central charges of SUSY algebras. The BPS domain walls in 3 þ 1-dimensional spacetime have been extensively studied in N ¼ 1 SUSY theories [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] and N ¼ 2 SUSY theories [37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54] (see Refs. [18,[55][56][57] as a review).…”