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We develop the background field method for studying classical and quantumaspects of N=3, d=3 Chern-Simons and matter theories in N=3 harmonicsuperspace. As one of the immediate consequences, we prove a nonrenormalizationtheorem implying the ultra-violet finiteness of the corresponding supergraphperturbation theory. We also derive the general hypermultiplet and gaugesuperfield propagators in a Chern-Simons background. The leading supergraphswith two and four external lines are evaluated. In contrast to thenon-supersymmetric theory, the leading quantum correction to the massivecharged hypermultiplet proves to be the super Yang-Mills action rather than theChern-Simons one. The hypermultiplet mass is induced by a constant triplet ofcentral charges in the N=3, d=3 Poincare superalgebra.

Quantum N=3, d=3 Chern-Simons Matter Theories in Harmonic Superspace