论文标题
2d Fermionic RCFT之间的Hecke关系
Hecke Relations among 2d Fermionic RCFTs
论文作者
论文摘要
最近，Harvey和Wu提出了一个合适的Hecke操作员，用于矢量值$ sl（2，\ Mathbb {z}）$模块化表单，以连接不同2D合理的共同字段理论（RCFTS）的字符。我们将这种操作员概括到2D费米子rcfts，并将其称为费米金Hecke操作员。新的Hecke操作员自然地将费米金理论的Neveu-Schwarz（NS）特征映射到另一种费米子理论的NS特征。从数学上讲，它是矢量值$γ_θ$模块化重量零的天然Hecke操作员。我们发现它也可以扩展到$ \ mathrm {\ widetilde {ns}} $和Ramond（R）扇区，通过将两个部门的字符相结合在一起。我们系统地研究了具有多达五个NS字符的2D费米子RCFT之间的费米克Hecke关系，发现几乎所有已知的超对称RCFTs都可以实现为一些简单理论的费米金Hecke图像，例如超对称的最小模型。我们还研究了费米金Hecke图像之间的cOSET关系。
Recently, Harvey and Wu proposed a suitable Hecke operator for vector-valued $SL(2,\mathbb{Z})$ modular forms to connect the characters of different 2d rational conformal field theories (RCFTs). We generalize such an operator to the 2d fermionic RCFTs and call it fermionic Hecke operator. The new Hecke operator naturally maps the Neveu-Schwarz (NS) characters of a fermionic theory to the NS characters of another fermionic theory. Mathematically, it is the natural Hecke operator on vector-valued $Γ_θ$ modular forms of weight zero. We find it can also be extended to $\mathrm{\widetilde{NS}}$ and Ramond (R) sectors by combining the characters of the two sectors together. We systematically study the fermionic Hecke relations among 2d fermionic RCFTs with up to five NS characters and find that almost all known supersymmetric RCFTs can be realized as fermionic Hecke images of some simple theories such as supersymmetric minimal models. We also study the coset relations between fermionic Hecke images with respect to $c=12k$ holomorphic SCFTs.
