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

Prove that the four-dimensional N=1 SU(N) gauge theory with one adjoint \Phi, two rank-2 antisymmetric A and two 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 \le 4.

Background

The a-maximization paper of this SU(N) Type III theory indicates unitary central charges and no operator decoupling across the range, motivating the conjecture of an interacting IR SCFT.

Type III models have near-engineering R-charges and a=c≈(1/4)dim G at large N.

References

We therefore conjecture that this theory describes an interacting SCFT for $0\leq N_f \leq 4$.

— Large N Universality of 4d N=1 SCFTs with Simple Gauge Groups (2510.19136 - Cho et al., 21 Oct 2025) in Section 4.17 (1 Adj + 2 A + 2 \overline{A} + Nf (Q + \overline{Q})), Conformal window