Existence of IR SCFT for Sp(N) Type III theory with three antisymmetric tensors and 2Nf fundamentals (exception at N=2, Nf=0)

Prove that the four-dimensional N=1 Sp(N) gauge theory with three rank-2 antisymmetric tensors A and 2Nf fundamental chiral multiplets Q (with superpotential W=0 and even number of fundamentals) flows to an interacting superconformal field theory in the infrared for all integers N and Nf satisfying 0 \le Nf \le 6, excluding the case (Nf,N)=(0,2).

Background

This Sp(N) Type III model parallels N=4-like matter combinations and shows a=c≈(1/2)dim G at large N. The authors note an exception at (Nf,N)=(0,2) where the theory does not flow to an interacting SCFT; otherwise, a-maximization supports the conjecture across the window.

Type III theories have sparse spectra and short flows.