Existence of IR SCFT for SU(N) with one adjoint, one symmetric and one conjugate antisymmetric plus chiral matter

Prove that the four-dimensional N=1 SU(N) gauge theory with one adjoint \Phi, one rank-2 symmetric S, one conjugate antisymmetric \widetilde{A}, (Nf+8) anti-fundamentals \widetilde{Q}, and Nf fundamentals Q (with superpotential W=0) flows to an interacting superconformal field theory in the infrared for all integers N and Nf satisfying 0 \le Nf \le N−4.

Background

This chiral SU(N) theory mixes adjoint and tensor matter with unequal fundamental multiplicities. The authors note that the top-of-window case Nf=N−4 has a non-trivial conformal manifold and that a-maximization is well-behaved for smaller Nf, motivating the conjecture of an interacting IR SCFT.

It belongs to the Type II universality class.