On the Vacua of Mass-deformed Gaiotto-Tomasiello Theories

We write explicit Lagrangian and supersymmetry transformation rules using the component fields in the $\mathcal{N}=2,3$ GT theories. In the component field expansion, the manifestation of an additional $\mathcal{N}=1$ supersymmetry is verified in the $\mathcal{N}=3$ GT theory. We find maximal supersymmetry preserving mass-deformation of the GT theories and their classical supersymmetric discrete vacua. Some interesting aspects of the set of discrete vacua are discussed in comparison with the ABJM case.