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We calculate the Witten index for 3d supersymmetric Yang-Mills-Chern-Simonstheories with matter. For N=2 theories, our results coincide with the resultsof recent [1]. We compare the situation in 3d to that in 4d N = 1 theories withmassive matter. In both cases, extra Higgs vacuum states may appear when theLagrangian involves nontrivial Yukawa interactions between the mattersuperfields. In addition, in 3d theories, massive fermion loops affect theindex via renormalization of the Chern-Simons level k.

Witten index in N=1 and N=2 SYMCS theories with matter