# Bootstrapping Mixed Correlators in 4D $\mathcal{N}=1$ SCFTs

## TL;DR

This paper employs the numerical conformal bootstrap to analyze mixed correlators in 4D $
=1$ SCFTs, deriving new superconformal blocks and constraints that suggest the existence of a special minimal SCFT solution.

## Contribution

It introduces new superconformal blocks and universal bounds for 4D $
=1$ SCFTs, advancing understanding of their operator spectrum and crossing symmetry constraints.

## Key findings

- New superconformal blocks for mixed correlators.
- Universal bounds indicating a special minimal SCFT.
- Evidence supporting a unique solution to crossing symmetry.

## Abstract

The numerical conformal bootstrap is used to study mixed correlators in $\mathcal{N}=1$ superconformal field theories (SCFTs) in $d=4$ spacetime dimensions. Systems of four-point functions involving scalar chiral and real operators are analyzed, including the case where the scalar real operator is the zero component of a global conserved current multiplet. New results on superconformal blocks as well as universal constraints on the space of 4D $\mathcal{N}=1$ SCFTs with chiral operators are presented. At the level of precision used, the conditions under which the putative "minimal" 4D $\mathcal{N}=1$ SCFT may be isolated into a disconnected allowed region remain elusive. Nevertheless, new features of the bounds are found that provide further evidence for the presence of a special solution to crossing symmetry corresponding to the "minimal" 4D $\mathcal{N}=1$ SCFT.