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The Higgs branch of N=2 supersymmetric gauge theories with non-Abelian gaugegroups are described by hyper-Kahler (HK) nonlinear sigma models with potentialterms. With the non-Abelian HK quotient by U(M) and SU(M) gauge groups, we givethe massive HK sigma models that are not toric in the N=1 superfield formalismand 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.Comment: 37 pages, one figure, final version to appear in Prog. Theor. Phy

Vacua of Massive Hyper-Kahler Sigma Models with Non-Abelian Quotient