A search for minimal 4d N=1 SCFT

TL;DR

The paper tackles the existence of a minimal interacting 4d ${\cal N}=1$ SCFT by constructing an explicit IR fixed point obtained from an ${\cal N}=1$ preserving deformation of the ${\cal N}=2$ ${A_2}$ Argyres–Douglas theory with a chiral primary $u$ satisfying $u^2=0$. The authors show that at the IR fixed point, $\Delta(u)=\tfrac{3}{2}$ and the chiral ring is finite, consisting of a small set of operators including $u$, $\lambda_\alpha$, $S$, and $uS$, with $u^2$ being trivial in the chiral ring. They compute the central charges to be $a=\frac{263}{768}$ and $c=\frac{271}{768}$, which satisfy the $a$-theorem and the bound $\tfrac{1}{2}<a/c<\tfrac{3}{2}$, supporting a nontrivial IR SCFT without accidental symmetries. The work discusses the gap with current conformal bootstrap bounds and outlines future directions, including 6d-constructed routes and other AD deformations, to further constrain or improve upon the minimal-model candidate.

Abstract

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 Δ(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.