Existence of IR SCFT for Sp(N) Type III theory with two symmetric and one antisymmetric tensor plus 2Nf fundamentals

Prove that the four-dimensional N=1 Sp(N) gauge theory with two rank-2 symmetric tensors S, one rank-2 antisymmetric tensor 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 < 2.

Background

This Sp(N) Type III theory exhibits near-free R-charges and universal large-N central charges (a=c≈(1/2)dim G for Sp(N) with two tensors). The a-maximization analysis supports the conjecture of an interacting IR SCFT for small Nf.

Type III models are likely to be holographic due to a=c and sparse spectra.

References

Thus, we conjecture that the theory flows to an interacting SCFT for $0\leq N_f < 2$.

— Large N Universality of 4d N=1 SCFTs with Simple Gauge Groups (2510.19136 - Cho et al., 21 Oct 2025) in Section 6.6 (2 S + 1 A + 2 Nf Q), Conformal window