Supersymmetric Tensor Model at Large $N$ and Small $\epsilon$

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.

arXiv comment30 pages, 5 figures

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• A 3d disordered superconformal fixed point
• Perturbative and Nonperturbative Studies of CFTs with MN Global Symmetry
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• The statistical mechanics of near-BPS black holes
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• Non-Perturbative Defects in Tensor Models from Melonic Trees
• The F-theorem in the melonic limit
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