Existence of IR SCFT for SU(N) with two symmetric pairs and Nf fundamentals

Prove that the four-dimensional N=1 SU(N) gauge theory with two rank-2 symmetric chiral multiplets S, two conjugate symmetric multiplets \widetilde{S}, and Nf pairs of fundamental Q and anti-fundamental \widetilde{Q} chiral multiplets (with superpotential W=0) flows under the renormalization group to an interacting superconformal field theory in the infrared for all integers N and Nf satisfying 0 \le Nf < N−4.

Background

The paper classifies large-N 4d N=1 SCFTs built from simple gauge groups and matter in rank-1 and rank-2 representations, with W=0 and fixed flavor symmetry. For the SU(N) theory with two symmetric and two conjugate symmetric tensors plus Nf fundamentals, a-maximization yields a unique solution, central charges satisfy the Hofman-Maldacena bounds, and no operators decouple along the flow, motivating a conjecture that the IR fixed point is an interacting SCFT across a range of Nf.

This family is one of the Type II theories, which exhibit universal large-N behavior with a=c at leading order and a sparse operator spectrum.