We derive a supersymmetric renormalization group (RG) equation for the scale-dependent superpotential of the supersymmetric OðNÞ model in three dimensions. For a supersymmetric optimized regulator function, we solve the RG equation for the superpotential exactly in the large-N limit. The fixed-point solutions are classified by an exactly marginal coupling. In the weakly coupled regime there exists a unique fixed-point solution, for intermediate couplings we find two separate fixed-point solutions and in the strong coupling regime no globally defined fixed-point potentials exist. We determine the exact critical exponents both for the superpotential and the associated scalar potential. Finally, we relate the hightemperature limit of the four-dimensional theory to the Wilson-Fisher fixed point of the purely scalar theory.
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