Identify the 2d CFT corresponding to (A1,Br) for general r

Identify, for general integers r≥2, the rational two-dimensional conformal field theories whose characters match the generalized Nahm sums associated with the pair of Dynkin diagrams (A1,B_r) as defined in the paper.

Background

Using Bressoud-type identities, the authors establish modularity for the generalized Nahm sums associated with (A1,Br) for all r≥2 and determine their central charge c(A1,B_r)=(2r−1)/(r+1).

Despite modularity, the precise identification of the corresponding CFT is unknown in general; only the cases r=2,3 are currently matched to specific CFTs in Section 3.