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In this paper we study the Nielsen identity for the supersymmetricChern-Simons-matter model in the superfield formalism, in three spacetimedimensions. The Nielsen identity is essential to understand the gaugeinvariance of the symmetry breaking mechanism, and it is calculated by usingthe BRST invariance of the model. We discuss the technical difficulties inapplying this identity to the complete effective superpotential, but we showhow we can study in detail the gauge independence of one part of the effectivesuperpotential, $K_{eff}$. We calculate the renormalization group functions ofthe model for arbitrary gauge-fixing parameter, finding them to be independentof the gauge choice. This result can be used to argue that $K_{eff}$ also doesnot depend on the gauge parameter. We discuss the possibility of the extensionof these results to the complete effective superpotential.

Nielsen Identity and the Renormalization Group Functions in an Abelian Supersymmetric Chern-Simons Model in the Superfield Formalism