Exploring the minimal 4D N=1 SCFT

We study the conformal bootstrap constraints for 4D 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 U(1)(R) current multiplet and estimating the central charge and low-lying operator spectrum of this theory.