Supersymmetric tensor model at large N and small ϵ

Abstract

We study the O(N)3 supersymmetric quantum field theory of a scalar superfield φabc 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 possibility of adding the Chern-Simons action to gauge the supersymmetric model.