来自强耦合四维无希格斯SCFT的无限族非有理VOA
An Infinite Family of Non-Rational VOAs from Strongly Coupled 4d Higgsless SCFTs
- Fudan University（复旦大学）
- Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS)（上海数学与交叉学科研究院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究一类具平凡希格斯分支的四维$\boldsymbol{\textit{N}=2}$ SCFT，提出其对应VOA为二重态代数$\boldsymbol{\textit{A}(4m+2)}$，通过验证舒尔指标与共形反常等建立了无希格斯SCFT与非有理VOA的系统联系。
AI中文摘要：
我们研究了一类无限族强耦合四维$\boldsymbol{\textit{N}=2}$超共形场论（SCFT），这类理论具有平凡希格斯分支，被称为$(A_2,D_{3m+1})$阿吉尔-道格拉斯理论。我们提出，它们对应的顶点算子代数（VOA）是二重态代数$\boldsymbol{\textit{A}(4m+2)}$，这是一类无限族非有理顶点算子超代数，具有仅含三个场的极其简单的强生成集。我们对该提议进行了多项高度非平凡的验证，特别是从VOA中重现了四维共形反常$a$和$c$，并解析证明了SCFT的舒尔指标与VOA的超特征标之间的精确相等关系。一个关键要素是通过两个更简单的构造块对$(A_2,D_{3m+1})$理论进行对角规范实现，这使得舒尔指标的计算变得可行。值得注意的是，我们发现$(A_2,D_{3m+1})$理论的舒尔指标与$\boldsymbol{\textit{N}=4}$ $SU(2)$超杨-米尔斯理论的舒尔指标一致，仅相差一个整体 prefactor 和 fugacities 的适当识别。我们还讨论了对双参数族$(A_{2s},D_{(2s+1)m+1})$的推广，该族成员同样具有平凡希格斯分支并允许对角规范实现。一个特别有趣的子族是$(A_{2s},D_{2s+2})$，其四维共形反常满足$a=c$。我们的结果揭示了无希格斯SCFT、对角规范以及强有限但非有理顶点算子代数之间的系统联系。
英文摘要：
We study an infinite family of strongly coupled four-dimensional $\mathcal N=2$ 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 $\mathcal A(4m+2)$, 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 $\mathcal N=4$ $SU(2)$ 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, $a=c$. Our results reveal a systematic connection between Higgsless SCFTs, diagonal gauging, and strongly finite but non-rational vertex operator algebras.
