  We study a supersymmetric tensor model with four supercharges and $O(N)^3$
global symmetry. The model is based on a chiral scalar superfield with three
indices and quartic tetrahedral interaction in the superpotential, which is
relevant below three dimensions. In the large-$N$ limit the model is dominated
by melonic diagrams. We solve the Dyson-Schwinger equations in superspace for
generic $d$ and extract the dimension of the chiral field and the dimensions of
bilinear operators transforming in various representations of $O(N)^3$. We find
that all operator dimensions are real and above the unitarity bound for
$1<d<3$. Our results also agree with perturbative results in $3-\varepsilon$
expansion. Finally, we extract the large spin behaviour of bilinear operators
and discuss the connection with lightcone bootstrap.
