A Family of Vertex Algebras from Argyres-Douglas Theory

Heeyeon Kim; Jaewon Song

doi:10.21468/SciPostPhys.19.6.144

paper

A Family of Vertex Algebras from Argyres-Douglas Theory

arXiv:2412.20015 · doi:10.21468/SciPostPhys.19.6.144

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 $Tr M^{N}$ 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-Cvitanović exceptional series type $(A_{2})_{1}$ , $(G_{2})_{1}$ , $(D_{4})_{1}$ , $(F_{4})_{1}$ , $(E_{6})_{1}$ from Argyres-Douglas theories. We also find the modular invariant characters of the `intermediate vertex algebras' $(E_{7 \frac{1}{2}})_{1}$ and $(X_{1})_{1}$ . 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.

29 pages, 6 figures, v4: fixed missing reference

A Family of Vertex Algebras from Argyres-Douglas Theory

Abstract

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