论文标题
Hecke-Langlands二元性和Witten的重力月光
Hecke-Langlands Duality and Witten's Gravitational Moonshine
论文作者
论文摘要
我们表明，关于Hecke eigenfields和eigensheaves的保形块有$ d = 2 $有理CFT的双重描述。特别是，可以从Hecke操作员的作用中重建分区功能，共形性字符和晶格theta函数。该方法可以应用于：1）配备痕迹（或反痕迹）形式的Galois数字字段的整数环； 2）仿射Kac-Moody代数和WZW模型的根晶格； 3）Belavin-Polyakov-Zamolodchikov的最小模型和相关的$ d = 2 $旋转链/晶格模型； 4）水ech和niemeier lattices等的顶点代数。我们还使用原始的Witten的想法来构建3维量子重力，作为$ C = 24 $ frenkel-Lepowsky-Meurman的ADS/CFT二重要。关于几何Langlands二重性，我们使用Beilinson-Drinfeld，Frenkel-Ben-Zvi，Gukov-Kapustin-Witten等结果（参见参考）。
We show that there is a dual description of conformal blocks of $d=2$ rational CFT in terms of Hecke eigenfields and eigensheaves. In particular, partition functions, conformal characters and lattice theta functions may be reconstructed from the action of Hecke operators. This method can be applied to: 1) rings of integers of Galois number fields equipped with the trace (or anti-trace) form; 2) root lattices of affine Kac-Moody algebras and WZW-models; 3) minimal models of Belavin-Polyakov-Zamolodchikov and related $d=2$ spin-chain/lattice models; 4) vertex algebras of Leech and Niemeier lattices and others. We also use the original Witten's idea to construct the 3-dimensional quantum gravity as the AdS/CFT-dual of $c=24$ Monster vertex algebra of Frenkel-Lepowsky-Meurman. Concerning the geometric Langlands duality, we use results of Beilinson-Drinfeld, Frenkel-Ben-Zvi, Gukov-Kapustin-Witten and many others (cf. references).
