We study non-linear σ models whose target spaces are the Higgs phases of supersymmetric SO and USp gauge theories by using the Kähler and hyper-Kähler quotient constructions. We obtain the explicit Kähler potentials and develop an expansion formula to make use of the obtained potentials from which we also calculate the curvatures of the manifolds. The 1/2 BPS lumps in the U (1) × SO and U (1) × USp Kähler quotients and their effective descriptions are also studied. In this connection, a general relation between moduli spaces of vortices and lumps is discussed. We find a new singular limit of the lumps with non-vanishing sizes in addition to the ordinary small lump singularity. The former is due to the existence of singular submanifolds in the target spaces.
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