We construct walls of mass-deformed Kähler nonlinear sigma models on SO(2N )/U (N ), by using the moduli matrix formalism and the simple roots of SO(2N ). Penetrable walls are observed in the nonlinear sigma models on SO(2N )/U (N )

We study the Bogomol'nyi-Prasad-Sommerfield wall solutions in massive Kähler nonlinear sigma models on SOð2NÞ=UðNÞ and SpðNÞ=UðNÞ in three-dimensional spacetime. We show that SOð2NÞ=UðNÞ and SpðNÞ=UðNÞ models have 2 NÀ1 and 2 N discrete vacua, respectively. We explicitly construct the exact BPS multiwall solutions for N 3.

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...

We study the holographic QCD in the hadronic medium by using the soft wall model. We discuss the Hawking-Page transition between Reissner-Nordström AdS black hole and thermal charged AdS of which the geometries correspond to deconfinement and confinement phases respectively. We also present the numerical result of the vector and axial vector meson spectra depending on the quark density. *

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