A family of vertex algebras from Argyres-Douglas theory

Abstract

We find that multiple vertex algebras can arise from a single 4d N = 2 superconformal field theory (SCFT). The connection is given by the BPS monodromy operator 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 TrMN yield modular functions that can be identified with the vacuum characters of certain vertex algebra for each N. In particular, we realize unitary VOAs of the Deligne-Cvitanovic exceptional series type (A2)1, (G2)1, (D4)1, (F4)1, (E6)1 from Argyres-Douglas theories. We also find the modular invariant characters of the 'intermediate vertex algebras' (E7 21 )1 and (X1)1. Our analysis allows us to construct 3d N = 2 gauge theories that flow to N = 4 SCFTs in the IR, whose specialized half-index can be identified with these modular invariant characters.