Exploring the Minimal 4D $\mathcal{N}=1$ SCFT

TL;DR

This paper investigates the constraints of 4D $ ext{N}=1$ superconformal bootstrap for theories with a chiral operator and the relation $ ext{phi}^2=0$, providing evidence for a minimal interacting SCFT with specific spectral properties.

Contribution

It offers a detailed analysis of a conjectured minimal 4D $ ext{N}=1$ SCFT, identifying key operator multiplets and estimating its central charge and spectrum.

Findings

Presence of a $ ext{U}(1)_R$ current multiplet in the solution

Estimated central charge of the minimal SCFT

Characterized low-lying operator spectrum

Abstract

We study the conformal bootstrap constraints for 4D $\mathcal{N}=1$ superconformal field theories containing a chiral operator $\phi$ and the chiral ring relation $\phi^2=0$. Hints for a minimal interacting SCFT in this class have appeared in previous numerical bootstrap studies. We perform a detailed study of the properties of this conjectured theory, establishing that the corresponding solution to the bootstrap constraints contains a $\text{U}(1)_R$ current multiplet and estimating the central charge and low-lying operator spectrum of this theory.