The Higgs branch of N = 2 supersymmetric gauge theories with non-Abelian gauge groups is described by hyper-Kähler (HK) nonlinear sigma models with potential terms. Using the non-Abelian HK quotient with respect to U(M) and SU(M) gauge groups, we derive the massive HK sigma models that are not toric in the N = 1 superfield formalism and the harmonic superspace formalism. The U(M) quotient gives N!/[M!(N - M)!] discrete vacua that may allow various types of domain walls, whereas the SU(M) quotient gives no discrete vacua.
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