A Family of Vertex Algebras from Argyres-Douglas Theory

TL;DR

<3-5 sentence high-level summary>

Abstract

We find that multiple vertex algebras can arise from a single 4d $\mathcal{N}=2$ 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 $\mathrm{Tr} M^N$ 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 $\mathcal{N}=2$ gauge theories that flow to $\mathcal{N}=4$ SCFTs in the IR, whose specialized half-index can be identified with these modular invariant characters.

Figures (6)

• Figure 1: BPS quiver for the $(A_1, A_2)$ theory
• Figure 2: BPS quiver for the $(A_1, A_3)$ theory in the canonical chamber
• Figure 3: BPS quiver for the $(A_1, A_4)$ theory in the linear chamber
• Figure 4: BPS quiver for the $(A_1, D_4)$ theory
• Figure 5: 'Quiver diagram' for the $"E_{7\frac{1}{2}}"$ theory. Each solid line corresponds to a mixed CS interaction with level $-1$ (not the bifundamental chiral multiplet), and each of the gauge group factors has the effective CS level $2$. The dashed line corresponds to the chiral multiplet whose charge is $1$.