A search for minimal 4d N=1 SCFT

We discuss a candidate for a minimal interacting 4-dimensional N=1 superconformal field theory (SCFT). 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 A2 Argyres-Douglas theory. The central charges are given by (a,c)=(263/768, 271/768) ~ (0.342,0.353). There is no moduli space of vacua, no flavor symmetry, and the chiral ring is finite.