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

TL;DR

This paper develops a conformal bootstrap approach for the three-dimensional ${ m extbf{N}=1}$ superconformal field theory, providing approximate operator dimensions and central charge values, with implications for experimental supersymmetry in 2+1 dimensions.

Contribution

It introduces a bootstrap method tailored for the ${ m extbf{N}=1}$ SCFT in three dimensions, extending previous analyses of the Ising model to supersymmetric theories.

Findings

Estimated conformal dimensions of several operators.

Calculated the central charge $C_T$ for the SCFT.

Results align well with previous theoretical estimates.

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}.