Supersymmetric tensor model at large <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math> and small <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ε</mml:mi></mml:math>

Abstract

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

Topics & Concepts