Conformal embedding under folding for CFTs from (A1,G) and (A1,G′)

Demonstrate that for a simply-laced Dynkin diagram G and its folding G′, the rational 2d conformal field theory associated (via the paper’s Nahm-sum/CFT correspondence) to the pair (A1,G′) is conformally embedded in the corresponding CFT associated to (A1,G), i.e., CFT(A1,G′)⊂CFT(A1,G).

Background

The authors observe that for foldings G→G′ the Coxeter numbers, and hence the central charges c(A1,G) and c(A1,G′), coincide, suggesting a structural relationship between the associated CFTs.

Motivated by numerous checks and decompositions of Nahm sums into characters, they conjecture a conformal embedding relating the folded and unfolded theories, which would in turn explain character decompositions and modular-invariant partition functions across the folding.

References

We further conjecture that the CFT associated with the folded one can be conformally embedded in the CFT associated with the unfolded one.

— Dynkin diagrams, generalized Nahm sums and 2d CFTs  (2604.00847 - Sun et al., 1 Apr 2026) in Conjecture 3.1 (labeled Conjecture \ref{conj:A1}), Section 3