Existence of IR SCFT for SU(N) with one adjoint and one symmetric pair plus Nf fundamentals

Prove that the four-dimensional N=1 SU(N) gauge theory with one adjoint chiral multiplet \Phi, one rank-2 symmetric S, one conjugate symmetric \widetilde{S}, and Nf pairs of fundamental Q and anti-fundamental \widetilde{Q} chiral multiplets (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−2.

Background

This SU(N) theory augments an adjoint with a symmetric pair and fundamentals. The authors observe that at the upper bound Nf=N−2 the theory has a conformal manifold, and for smaller Nf the a-maximization analysis is well behaved, leading to the conjecture of an interacting IR SCFT throughout the range.

It is part of the Type II class, exhibiting a=c at leading order and sparse operator spectra.