Existence of IR SCFT for SU(N) with mixed symmetric/antisymmetric tensors and chiral matter

Prove that the four-dimensional N=1 SU(N) gauge theory with one rank-2 symmetric chiral multiplet S, two conjugate symmetric multiplets \widetilde{S}, one rank-2 antisymmetric chiral multiplet A, Nf+8 fundamentals Q, and Nf anti-fundamentals \widetilde{Q} (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−6.

Background

This chiral SU(N) theory includes asymmetric numbers of fundamentals and anti-fundamentals together with rank-2 tensors. The authors’ large-N analysis and a-maximization indicate well-behaved central charges and no decoupled operators for small Nf, leading them to conjecture the existence of an interacting IR SCFT within a specified Nf window.

The case belongs to the Type II universality class (a=c at leading order and sparse spectrum).