An Infinite Family of Non-Rational VOAs from Strongly Coupled 4d Higgsless SCFTs
Abstract
We study an infinite family of strongly coupled four-dimensional 𝒩=2 superconformal field theories (SCFTs) distinguished by a trivial Higgs branch, known as the (A2,D3m+1) Argyre-Douglas theories. We propose that their associated vertex operator algebras (VOAs) are the doublet algebras 𝒜(4m+2), an infinite family of non-rational vertex operator superalgebras with a remarkably simple strong generating set of only three fields. We provide several highly nontrivial checks of this proposal. In particular, we reproduce the four-dimensional conformal anomalies a and c from the VOA and analytically prove the exact equality between the Schur index of the SCFT and the supercharacter of the VOA. A key ingredient is a diagonal-gauging realization of the (A2,D3m+1) theories in terms of two simpler building blocks, which makes the Schur-index computation tractable. Remarkably, we find that the resulting Schur index of the (A2,D3m+1) theory coincides with that of 𝒩=4 SU(2) Super-Yang-Mills theory, up to an overall prefactor and an appropriate identification of fugacities. We also discuss a generalization to the two-parameter family (A2s,D(2s+1)m+1), whose members likewise have trivial Higgs branches and admit diagonal-gauging realizations. A particularly interesting subfamily is (A2s,D2s+2), for which the four-dimensional conformal anomalies coincide, a=c. As a byproduct, we also show that the doublet VOA 𝒜(4m+2) is not classically free for positive integer $m $. Our results reveal a systematic connection between Higgsless SCFTs, diagonal gauging, and strongly finite but non-rational vertex operator algebras.
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BibTeX
@misc{jiang2026infinite,
title = {{An Infinite Family of Non-Rational VOAs from Strongly Coupled 4d Higgsless SCFTs}},
author = {Hongliang Jiang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.02437},
eprint = {2609.02437},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02437},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An Infinite Family of Non-Rational VOAs from Strongly Coupled 4d Higgsless SCFTs
AU - Hongliang Jiang
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2609.02437
UR - https://arxiv.org/abs/2609.02437
AB - We study an infinite family of strongly coupled four-dimensional 𝒩=2 superconformal field theories (SCFTs) distinguished by a trivial Higgs branch, known as the (A_2,D_3m+1) Argyre-Douglas theories. We propose that their associated vertex operator algebras (VOAs) are the doublet algebras 𝒜(4m+2), an infinite family of non-rational vertex operator superalgebras with a remarkably simple strong generating set of only three fields. We provide several highly nontrivial checks of this proposal. In particular, we reproduce the four-dimensional conformal anomalies a and c from the VOA and analytically prove the exact equality between the Schur index of the SCFT and the supercharacter of the VOA. A key ingredient is a diagonal-gauging realization of the (A_2,D_3m+1) theories in terms of two simpler building blocks, which makes the Schur-index computation tractable. Remarkably, we find that the resulting Schur index of the (A_2,D_3m+1) theory coincides with that of 𝒩=4 SU(2) Super-Yang-Mills theory, up to an overall prefactor and an appropriate identification of fugacities. We also discuss a generalization to the two-parameter family (A_2s,D_(2s+1)m+1), whose members likewise have trivial Higgs branches and admit diagonal-gauging realizations. A particularly interesting subfamily is (A_2s,D_2s+2), for which the four-dimensional conformal anomalies coincide, a=c. As a byproduct, we also show that the doublet VOA 𝒜(4m+2) is not classically free for positive integer $m $. Our results reveal a systematic connection between Higgsless SCFTs, diagonal gauging, and strongly finite but non-rational vertex operator algebras.
ER -