A large-N tensor model with four supercharges

Abstract

Abstract We study a supersymmetric tensor model with four supercharges and O(N)3 global symmetry. The model is based on a chiral scalar superfield with three indices and quartic tetrahedral interaction in the superpotential, which is relevant below three dimensions. In the large-N limit the model is dominated by melonic diagrams. We solve the Dyson-Schwinger equations in superspace for generic d and extract the dimension of the chiral field and the dimensions of bilinear operators transforming in various representations of O(N)3. We find that all operator dimensions are real and above the unitarity bound for 1 < d < 3. Our results also agree with perturbative results in 3 − ε expansion. Finally, we extract the large spin behaviour of bilinear operators and discuss the connection with lightcone bootstrap.