A large-$N$ tensor model with four supercharges

TL;DR

This paper investigates a supersymmetric tensor model with four supercharges and $O(N)^3$ symmetry, solving for operator dimensions and analyzing its behavior across dimensions, revealing consistent and real spectra.

Contribution

It introduces and solves a large-$N$ supersymmetric tensor model with four supercharges, providing explicit operator dimensions and connecting with bootstrap results.

Findings

Operator dimensions are real and above unitarity bounds for 1<d<3.

Results agree with perturbative $3- ext{epsilon}$ expansion.

Large spin behavior of bilinear operators analyzed.

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 $3-\varepsilon$ expansion. Finally, we extract the large spin behaviour of bilinear operators and discuss the connection with lightcone bootstrap.