论文标题
费米金有理保形场理论和模块化线性微分方程
Fermionic Rational Conformal Field Theories and Modular Linear Differential Equations
论文作者
论文摘要
我们为级别的TWO元素子组定义模块化线性微分方程（MLDE）$γ_\ vartheta $，$γ^0（2）$和$γ_0（2）$ of $ \ text {sl} _2 _2 _2 _2 _2 _2（\ mathbb z）$。每个亚组对应于圆环上的一个自旋结构之一。 Fermionic MLDE的极点结构是通过为级别的两个一致性亚组利用价值公式来研究的。我们专注于没有杆子的第一阶和二阶Holomorthic MLDES，并使用它们来找到一类“ Fermionic Rative Roncation Condormal Field Theories”，它们在$ q $ sermeries扩展其角色中具有非负整数系数。我们研究了这些费米子RCFT的详细特性，其中一些是超对称的。这项工作还为费米子模块化张量类别的分类提供了一个起点。
We define Modular Linear Differential Equations (MLDE) for the level-two congruence subgroups $Γ_\vartheta$, $Γ^0(2)$ and $Γ_0(2)$ of $\text{SL}_2(\mathbb Z)$. Each subgroup corresponds to one of the spin structures on the torus. The pole structures of the fermionic MLDEs are investigated by exploiting the valence formula for the level-two congruence subgroups. We focus on the first and second order holomorphic MLDEs without poles and use them to find a large class of `Fermionic Rational Conformal Field Theories', which have non-negative integer coefficients in the $q$-series expansion of their characters. We study the detailed properties of these fermionic RCFTs, some of which are supersymmetric. This work also provides a starting point for the classification of the fermionic Modular Tensor Category.
