  We study the $O(N)^3$ supersymmetric quantum field theory of a scalar
superfield $\Phi_{abc}$ with a tetrahedral interaction. In the large $N$ limit
the theory is dominated by the melonic diagrams. We solve the corresponding
Dyson-Schwinger equations in continuous dimensions below $3$. For sufficiently
large $N$ we find an IR stable fixed point and computed the $3-\epsilon$
expansion up to the second order of perturbation theory, which is in agreement
with the solution of DS equations. We also describe the $1+\epsilon$ expansion
of the model and discuss the possiblity of adding the Chern-Simons action to
gauge the supersymmetric model.
