Test the strong-rationality conjecture for Higgsless SCFTs

Establish or refute the conjecture that a four-dimensional superconformal field theory with trivial Higgs branch has a strongly rational associated VOA when all Coulomb-branch operator dimensions are non-integral, and a strongly finite but non-rational associated VOA otherwise.

Background

The paper proposes that the (A_2,D_{3m+1}) theories, which have trivial Higgs branches, correspond to the non-rational doublet VOAs A(4m+2). This motivates a broader relationship between the arithmetic of Coulomb-branch dimensions and the rationality properties of associated VOAs.

The stated conjecture predicts a dichotomy: non-integral Coulomb dimensions should lead to strongly rational VOAs, whereas the presence of integral Coulomb dimensions should instead lead to strongly finite but non-rational VOAs. The claim is presented as a general conjecture and is not established in the paper.

References

Motivated by known examples, we conjecture that, for SCFTs with trivial Higgs branch, the associated VOA is strongly rational if all the Coulomb dimensions are non-integral, and strongly finite but non-rational otherwise.

— An Infinite Family of Non-Rational VOAs from Strongly Coupled 4d Higgsless SCFTs  (2609.02437 - Jiang, 2 Sep 2026) in Section 6, “Conclusion”