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

## TL;DR

This paper analyzes a supersymmetric tensor model with tetrahedral interactions at large N, solving Dyson-Schwinger equations in continuous dimensions, and explores its fixed points and possible gauge extensions.

## Contribution

It provides the first detailed analysis of the supersymmetric tensor model's IR fixed points and perturbative expansions in non-integer dimensions.

## Key findings

- Identified an IR stable fixed point in the large N limit.
- Computed the 3−ε expansion up to second order.
- Discussed potential gauge extensions with Chern-Simons action.

## 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.