Existence of IR SCFT for Sp(N) with two antisymmetric tensors and 2Nf fundamentals (exceptions at small N)

Prove that the four-dimensional N=1 Sp(N) gauge theory with two 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 N+5, excluding the cases (Nf,N)=(0,2), (0,3), and (1,2).

Background

This Sp(N) Type II model with antisymmetric tensors generally shows well-behaved a-maximization and unitary central charges, but certain small-N cases fail (either confining or non-unitary). Outside those exceptions, the authors conjecture the existence of an interacting IR SCFT across the window.

It maintains Type II universality with a=c in the large-N limit.

References

We therefore conjecture that this theory flows to an interacting SCFT for $0\leq N_f \leq N+5$, with the exception of $(N_f,N)=(0,2), (0,3), (1,2)$.

— Large N Universality of 4d N=1 SCFTs with Simple Gauge Groups (2510.19136 - Cho et al., 21 Oct 2025) in Section 6.5 (2 A + 2 Nf Q), Conformal window