Mixed Correlator 4D N=1 Superconformal Bootstrap

The numerical conformal bootstrap program has produced a wide range of impressive results concerning conformal field theories in various spacetime dimensions. In this talk I will focus on an application of this program to four-dimensional conformal theories with N=1 supersymmetry. In such theories a kink was found some time ago in the upper bound on the dimension of the first real scalar operator that appears in the operator product expansion of a chiral operator with its conjugate. Kinks signify isolated solutions to crossing equations, and are typically associated with specific conformal field theories. The nature of the putative theory at the N=1 kink remains mysterious. In this talk I will present numerical results concerning 4D N=1 theories using mixed correlation functions, and provide ample evidence that a special conformal field theory lives at the kink.