A large-$N$ tensor model with four supercharges

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.

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