Existence of IR SCFT for SU(N) Type III theory with three antisymmetric pairs plus Nf fundamentals

Prove that the four-dimensional N=1 SU(N) gauge theory with three rank-2 antisymmetric A and three conjugate antisymmetric \widetilde{A} chiral multiplets, and Nf pairs of fundamental Q and anti-fundamental \widetilde{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 < 6.

Background

This SU(N) Type III model parallels N=4 matter content in rank-2 form and shows a=c≈(1/4)dim G at large N with sparse spectra. The a-maximization analysis is consistent with an interacting IR SCFT across the stated Nf range.

These theories are potentially holographic and exhibit short flows.