Bootstrapping the $\cN=1$ SCFT in three dimensions

TL;DR

This work applies the 3D conformal bootstrap program to the minimal ${ m N}=1$ SCFT by leveraging the Ising-model bootstrap results (CBCB3) and incorporating SUSY constraints. The model is realized as the IR fixed point of a real scalar supermultiplet with superpotential $W=\

Abstract

We suggest a way to implement conformal bootstrap program for the case of the ${\cal N}=1$ SCFT in three dimensions using the previous analysis of the Ising model in \cite{CB}. We find approximate values for the conformal dimensions of several operators and the central charge $C_T$, the coefficient in the two-point function of the stress-tensor. Bootstrapping this particular (minimal) SCFT is of special interest as it was suggested in \cite{CM} that it may realize supersymmetry in 2+1 dimensions in experiment. The values are in a good agreement with the previous estimate in \cite{CM}.