Identify the VOAs of the T(4,3) and T(6,5) Higgsless theories

Identify the vertex operator algebras associated with the Higgsless theories T(4,3) and T(6,5), labelled by the coprime integers (p,N)=(4,3) and (6,5), respectively.

Background

The paper discusses the family of theories T(p,N), with p in {2,3,4,6}, that satisfy a=c. Among the Higgsless members, T(3,2) is identified with the (A_2,D_4) theory and has the A(6) chiral algebra.

In contrast, the associated VOAs for T(4,3) and T(6,5) have not been determined. The paper identifies determining these two chiral algebras as a particularly interesting unresolved problem.

References

The first, T(3,2), can be identified with the (A2, D4) theory corresponding to A(6) chiral algebra, whereas the VOAs associated with T(4,3) and T(6,5) remain unknown and would be particularly interesting to determine.

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

In the Lagrangian setting, Higgsless SCFTs were classified in Ref. [20], where, in particular, two infinite families were identified, although their associated VOAs remain unknown.

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