N=4 Chern-Simons theories with auxiliary vector multiplets
  We investigate a class of quiver-type Chern-Simons gauge theories with some Chern-Simons couplings vanishing. The vanishing of the couplings means that the corresponding vector fields are auxiliary fields. We show that these theories possess N=4 supersymmetry by writing down the actions and the supersymmetry transformation in terms of component fields in manifestly Spin(4) covariant form. 
Yosuke Imamura and Keisuke Kimura