Supersymmetric Tensor Model at Large $N$ and Small $ε$

We study the $O(N)^3$ supersymmetric quantum field theory of a scalar superfield $Φ_{abc}$ 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 $3-ε$ expansion up to the second order of perturbation theory, which is in agreement with the solution of DS equations. We also describe the $1+ε$ expansion of the model and discuss the possiblity of adding the Chern-Simons action to gauge the supersymmetric model.

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