TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.19.6.144
TI  - A family of vertex algebras from Argyres-Douglas theory
PY  - 2025/12/02
UR  - https://www.scipost.org/SciPostPhys.19.6.144
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 19
IS  - 6
SP  - 144
A1  - Kim, Heeyeon
AU  - Song, Jaewon
AB  - 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 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.
ER  -

@Article{10.21468/SciPostPhys.19.6.144,
	title={{A family of vertex algebras from Argyres-Douglas theory}},
	author={Heeyeon Kim and Jaewon Song},
	journal={SciPost Phys.},
	volume={19},
	pages={144},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.19.6.144},
	url={https://scipost.org/10.21468/SciPostPhys.19.6.144},
}