A family of vertex algebras from Argyres-Douglas theory

We find that multiple vertex algebras can arise from a single 4d N=2 𝒩 = 2 superconformal field theory (SCFT). The connection is given by the BPS monodromy operator M M , which is a wall-crossing invariant quantity that captures the BPS spectrum on the Coulomb branch. For a class of low-rank Argyres-Douglas theories, we find that the trace of the multiple powers of the monodromy operator Tr M^N M N yield modular functions that can be identified with the vacuum characters of certain vertex algebra for each N N . In particular, we realize unitary VOAs of the Deligne-Cvitanović exceptional series type (A_2)_1 ( A 2 ) 1 , (G_2)_1 ( G 2 ) 1 , (D_4)_1 ( D 4 ) 1 , (F_4)_1 ( F 4 ) 1 , (E_6)_1 ( E 6 ) 1 from Argyres-Douglas theories. We also find the modular invariant characters of the ‘intermediate vertex algebras’ (E71/2)_1 ( E 7 1 2 ) 1 and (X_1)_1 ( X 1 ) 1 . Our analysis allows us to construct 3d N=2 <