A 3d disordered superconformal fixed point

TL;DR

This paper explores a three-dimensional disordered supersymmetric field theory, demonstrating it flows to a superconformal fixed point with calculable spectral data, and compares results with conformal bootstrap predictions.

Contribution

It introduces a novel 3D disordered supersymmetric model and analytically characterizes its infrared superconformal fixed point with spectral data and operator coefficients.

Findings

Flow to a strongly coupled superconformal fixed point

Computed spectral data and operator product coefficients

Results are consistent with conformal bootstrap predictions

Abstract

We initiate the study of a three dimensional disordered supersymmetric field theory. Specifically, we consider a $\mathcal{N}=2$ large $N$ Wess-Zumino like model with cubic superpotential involving couplings drawn from a Gaussian random ensemble. Taking inspiration from analyses of lower dimensional SYK like models we demonstrate that the theory flows to a strongly coupled superconformal fixed point in the infra-red. In particular, we obtain leading large $N$ spectral data and operator product coefficients at the critical point. Moreover, the analytic control accorded by the model allows us to compare our results against those derived in the conformal bootstrap program and demonstrate consistency with general expectations.