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Recently, $$ \mathcal{N} $$ = 3 mass-deformed ABJM model with arbitrary mass-function depending on a spatial coordinate was constructed. In addition to the $$ \mathcal{N} $$ = 3 case, we construct lower supersymmetric $$ \mathcal{N} $$ = 1 and $$ \mathcal{N} $$ = 2 inhomogeneously mass-deformed ABJM (ImABJM) models, which require three and two arbitrary mass-functions, respectively. We also construct general vacuum solutions of the $$ \mathcal{N} $$ = 3 ImABJM model for any periodic mass-function. There are two classes of vacua, which are diagonal type and GRVV type according to reference value of mass-functions. We provide explicit examples of the vacuum solutions and discuss related operators.

Aspects of massive ABJM models with inhomogeneous mass parameters