Search for a Minimal N=1 Superconformal Field Theory in 4D

We discuss a candidate for a minimal interacting four-dimensional N = 1 superconformal field theory. The model contains a chiral primary operator u satisfying the chiral ring relation u(2) = 0, and its scaling dimension is Delta(u) = 1.5. The model is derived by turning on a N = 1 preserving deformation of N = 2 A(2) Argyres-Douglas theory. The central charges are given by (a, c) = (263/768, 271/768) similar or equal to (0.342, 0.353). There is no moduli space of vacua, no flavor symmetry, and the chiral ring is finite.