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A Family of Vertex Algebras from Argyres-Douglas Theory
by Heeyeon Kim, Jaewon Song
Submission summary
| Authors (as registered SciPost users): | Heeyeon Kim |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2412.20015v4 (pdf) |
| Date accepted: | Nov. 20, 2025 |
| Date submitted: | Oct. 14, 2025, 9:44 a.m. |
| Submitted by: | Heeyeon Kim |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Observational |
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-Cvitanovi\'c 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.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
List of changes
- We rewrote the first paragraph of Section 3 and the first paragraph of Section 3.1.3 to emphasize that the identification of the boundary VOA for these non-Lagrangian TFTs relies on assumptions about the IR SCFT and more importantly the deformability of the associated boundary conditions, which require careful examination.
- We also added a new paragraph on page 23, beginning with “The UV boundary condition…,” which reiterates this open problem and notes that it will be addressed in future work.
- A new reference [64] has been added.
- To better reflect the subtle and intricate nature of the intermediate algebras, we replaced “Vertex Operator Algebra” with “Vertex Algebra” in several places, including the title and the abstract.
- The paragraph surrounding Eq. (1.2) has been slightly revised.
- Minor typographical errors have been corrected.
Published as SciPost Phys. 19, 144 (2025)
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