论文标题
三维纯重力和广义Hecke操作员
Three Dimensional Pure Gravity and Generalized Hecke Operators
论文作者
论文摘要
在本文中，我们研究了ADS3中与纯重力相关的数学功能。模块化协方差将严格的约束放在此类功能的空间上；模块化不变性对如何将它们合并为物理可行的候选分区功能更加强大。我们明确详细介绍了全体形态和抗塑形功能的列表，这些功能是手性和抗手续分区函数的候选物，并注意到模块化协方差仅在左侧（resp。右）中央电荷是8，$ c \ in 8，$ c \ in 8 \ mathbbbbbb {n} n} $时。然后，我们在大部分广告中发现了对相应拓扑，chern-simons的对称组的相关约束。该理论的对称群可以是两个选择之一：$ so（2; 1）\ times so（2; 1）$或其对角线覆盖率三倍。我们介绍了广义的Hecke运算符，该操作员将模块化协变功能映射到模块化协变功能。通过这些数学结果，当手性中央电荷为八个时，我们获得了极端CFT2S的猜想分区函数以及相应的微型熵熵。最后，我们通过这些猜想的分区功能计算了散装重力理论中的贝肯斯坦 - 鹰熵的转向校正
In this paper, we study mathematical functions of relevance to pure gravity in AdS3. Modular covariance places stringent constraints on the space of such functions; modular invariance places even stronger constraints on how they may be combined into physically viable candidate partition functions. We explicitly detail the list of holomorphic and anti-holomorphic functions that serve as candidates for chiral and anti-chiral partition functions and note that modular covariance is only consistent with such functions when the left (resp. right) central charge is an integer multiple of 8, $c\in 8\mathbb{N}$. We then find related constraints on the symmetry group of the corresponding topological, Chern-Simons, theory in the bulk of AdS. The symmetry group of the theory can be one of two choices: either $SO(2; 1) \times SO(2; 1)$ or its three-fold diagonal cover. We introduce the generalized Hecke operators which map the modular covariant functions to the modular covariant functions. With these mathematical results, we obtain conjectural partition functions for extremal CFT2s, and the corresponding microcanonical entropies, when the chiral central charges are multiples of eight. Finally, we compute subleading corrections to the Beckenstein-Hawking entropy in the bulk gravitational theory with these conjectural partition functions
