论文标题
Hecke关系，coset和2D rcfts的分类
Hecke Relations, Cosets and the Classification of 2d RCFTs
论文作者
论文摘要
我们从系统地研究了Hecke关系，并在2D合理的共同场理论（RCFTS）中具有多达七个字符的$ C = 8K $ coset关系。我们建议，任何2D RCFT的字符 - 单一或非自动 - 满足霍明型模块化线性微分方程（MLDE）的特征，可以实现为Hecke图像或Hecke图像相对于$ C = 8K $理论的Hecke图像的库。受益于最新的Holomorthic Modular Bootstrap的结果，我们检查了所有可允许的理论，最多可容纳五个字符。我们还发现了许多新有趣的Hecke关系。例如，WZW模型的字符$（e_ {6}）_ 2，（e_7）_2，（e_ {7 \ frac12}）_ 2 $可以实现为Hecke Images $ \ Mathsf {t} _ {13} _ {13}， Virasoro最小型号$ M _ {\ rm sub}（7,6），m（5,4），m _ {\ rm eff}（13,2）$。此外，我们发现与第二大Fisher Group $ fi_ {23} $和Harada-Norton组$ Hn $相关的字符可以实现为Hecke Images $ \ Mathsf {t} _ {23}，\ Mathsf {t} _ {t} _ {199} $ M _ {\ rm eff}（7,2）$和$ m _ {\ rm eff}（7,2）^{\ otimes 2} $。从数学上讲，我们的研究提供了许多有趣的矢量值模块化功能的示例，最高为第七。
We systemically study the Hecke relations and the $c=8k$ coset relations among 2d rational conformal field theories (RCFTs) with up to seven characters. We propose that the characters of any 2d RCFT -- unitary or non-unitary -- satisfying a holomorphic modular linear differential equation (MLDE) can be realized as either a Hecke image or the coset of a Hecke image with respect to a $c=8k$ theory. Benefited from the recent results on holomorphic modular bootstrap, we check this proposal for all admissible theories with up to five characters. We also find many new interesting Hecke relations. For example, the characters of WZW models $(E_{6})_2,(E_7)_2,(E_{7\frac12})_2$ can be realized as the Hecke images $\mathsf{T}_{13},\mathsf{T}_{19},\mathsf{T}_{19}$ of Virasoro minimal models $M_{\rm sub}(7,6),M(5,4),M_{\rm eff}(13,2)$ respectively. Besides, we find the characters associated to the second largest Fisher group $Fi_{23}$ and the Harada-Norton group $HN$ can be realized as the Hecke images $\mathsf{T}_{23},\mathsf{T}_{19}$ of the product theories $M_{\rm eff}(5,2)\otimes M_{\rm eff}(7,2)$ and $M_{\rm eff}(7,2)^{\otimes 2}$ respectively. Mathematically, our study provides a great many interesting examples of vector-valued modular functions up to rank seven.
