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

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 fourpoint 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.