Existence of IR SCFT for SU(N) Type III theory with one symmetric pair and two antisymmetric pairs plus Nf fundamentals

Prove that the four-dimensional N=1 SU(N) gauge theory with one rank-2 symmetric S and one conjugate symmetric \widetilde{S}, two rank-2 antisymmetric A and two conjugate antisymmetric \widetilde{A}, 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 < 2.

Background

This SU(N) Type III theory exhibits near-free R-charges (≈2/3) and universal large-N central charges (a=c≈(1/4)dim G), indicating a sparse spectrum and short RG flows. A-maximization supports the conjecture of an interacting IR SCFT for very small Nf.

Type III theories are candidates for holography due to a=c and sparse spectra.