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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.… Click to show full abstract
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.
Journal Title: Physical Review D
Year Published: 2020
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