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Register a new userVacua and walls of mass-deformed Kahler nonlinear sigma models on $Sp(N)/U(N)$
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We study vacua and walls of mass-deformed Kahler nonlinear sigma models on $Sp(N)/U(N)$. We identify elementary walls with the simple roots of $USp(2N)$ and discuss compressed walls, penetrable walls and multiwalls by using the moduli matrix formalism.
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We holomorphically embed nonlinear sigma models (NLSMs) on $SO(2N)/U(N)$ and $Sp(N)/U(N)$ in the hyper-K{a}hler (HK) NLSM on the cotangent bundle of the Grassmann manifold $T^ast G_{2N,N}$, which is defined by $G_{N+M,M}=frac{SU(N+M)}{SU(N)times SU(M)times U(1)}$, in the ${mathcal{N}}=1$ superspace formalism and construct three-pronged junctions of the mass-deformed NLSMs (mNLSMs) in the moduli matrix formalism (MMF) by using a recently proposed method.
We study vacua, walls and three-pronged junctions of mass-deformed nonlinear sigma models on $SO(2N)/U(N)$ and $Sp(N)/U(N)$ for generic $N$. We review and discuss the on-shell component Lagrangians of the ${mathcal{N}}=2$ nonlinear sigma model on the Grassmann manifold, which are obtained in the ${mathcal{N}}=1$ superspace formalism and in the harmonic superspace formalism. We also show that the K{a}hler potential of the ${mathcal{N}}=2$ nonlinear sigma model on the complex projective space, which is obtained in the projective superspace formalism, is equivalent to the K{a}hler potential of the ${mathcal{N}}=2$ nonlinear sigma model with the Fayet-Iliopoulos parameters $c^a=(0,0,c=1)$ on the complex projective space, which is obtained in the ${mathcal{N}}=1$ superspace formalism.
We construct walls of mass-deformed K{a}hler 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 $SO(2N)/U(N)$ with $N>3$.
We analyse the geometry of four-dimensional bosonic manifolds arising within the context of $N=4, D=1$ supersymmetry. We demonstrate that both cases of general hyper-Kahler manifolds, i.e. those with translation or rotational isometries, may be supersymmetrized in the same way. We start from a generic N=4 supersymmetric three-dimensional action and perform dualization of the coupling constant, initially present in the action. As a result, we end up with explicit component actions for $N=4, D=1$ nonlinear sigma-models with hyper-Kahler geometry (with both types of isometries) in the target space. In the case of hyper-Kahler geometry with translational isometry we find that the action possesses an additional hidden N=4 supersymmetry, and therefore it is N=8 supersymmetric one.
We consider supersymmetric domain walls of four-dimensional $mathcal{N}!=!1$ $Sp(N)$ SQCD with $F!=!N+1$ and $F!=!N+2$ flavors. First, we study numerically the differential equations defining the walls, classifying the solutions. When $F!=!N+2$, in the special case of the parity-invariant walls, the naive analysis does not provide all the expected solutions. We show that an infinitesimal deformation of the differential equations sheds some light on this issue. Second, we discuss the $3d$ $mathcal{N}!=!1$ Chern-Simons-matter theories that should describe the effective dynamics on the walls. These proposals pass various tests, including dualities and matching of the vacua of the massive $3d$ theory with the $4d$ analysis. However, for $F!=!N+2$, the semiclassical analysis of the vacua is only partially successful, suggesting that yet-to-be-understood strong coupling phenomena are into play in our $3d$ $mathcal{N}!=!1$ gauge theories.
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