发表机构
Fudan University; Sun Yat-Sen University（复旦大学; 中山大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究秩一4d $\mathcal{N}=3$ SCFT的VOA表示论，通过MLDE和自由场实现获得Schur指标与特征标的闭式解，并推广到离散商理论。
AI 中文摘要
我们研究了与秩一4d $\mathcal{N} = 3$ 超共形场论相关的顶点算子代数（VOA）的表示论。对于 $\mathbb{Z}_3$ S-fold理论，其VOA $\mathcal{W}_{\mathbb{Z}_3}$ 的中心荷为 $c_{\mathrm{2d}} = -15$，我们利用 $\mathcal{N} = 1$ 拉格朗日描述，以Dedekind eta函数形式获得无味Schur指标，而Wilson圈指标给出无味非真空特征标。这些特征标均满足一个模线性微分方程（MLDE），其解空间还包含一个对数特征标。结合来自零态的带味MLDE与Zhu的结合代数以及自由场实现，我们研究了 $\mathcal{W}_{\mathbb{Z}_3}$ 的四个最高权模及其闭式带味特征标。类似的分析适用于通过对 $\mathcal{N} = 4$ $U(1)$ 和 $SU(2)$ 超杨-米尔斯理论的离散 $\mathbb{Z}_n$ 味子群进行规范得到的 $\mathcal{N} = 3$ 理论，对于这些理论，我们还获得了闭式Schur指标以及 $\mathbb{Z}_4$ 商VOA的一个新的自由场实现。
英文摘要
We study the representation theory of the vertex operator algebras (VOAs) associated with rank-one 4d $\mathcal{N} = 3$ superconformal field theories. For the $\mathbb{Z}_3$ S-fold theory, whose VOA $\mathcal{W}_{\mathbb{Z}_3}$ has central charge $c_{\mathrm{2d}} = -15$, we use the $\mathcal{N} = 1$ Lagrangian description to obtain the unflavored Schur index in terms of Dedekind eta functions, while Wilson-loop indices yield the unflavored non-vacuum characters. These characters all solve a modular linear differential equation (MLDE) whose solution space also contains a logarithmic character. Combining flavored MLDEs from null states with Zhu's associative algebra and a free-field realization, we study four highest-weight modules of $\mathcal{W}_{\mathbb{Z}_3}$ and their flavored characters in closed form. A parallel analysis applies to the $\mathcal{N} = 3$ theories obtained by gauging a discrete $\mathbb{Z}_n$ flavor subgroup of $\mathcal{N} = 4$ $U(1)$ and $SU(2)$ super-Yang--Mills, for which we also obtain closed-form Schur indices and a new free-field realization of the VOA of the $\mathbb{Z}_4$ quotient.
Comments64 pages;
