量子引力、黑洞、椭圆类和李代数同调的配分函数
Partition Functions for Quantum Gravity, Black Holes, Elliptic Genera and Lie Algebra Homologies
摘要：
在场论的量子生成函数和与合适的李代数的链和同调的维数相关的形式幂级数之间有着显著的联系。我们讨论了这种联系的同调方面，它的应用程序的最小三维引力的时空渐近AdS 3，这也描述了三维欧几里德黑洞，纯N = 1的超引力，和西格玛模型的N倍广义对称产品的配分函数。在同一背景下，我们还考虑了一些超对称西格玛模型的椭圆形属。这些例子可以被认为是模形式和谱函数（具有SL（2，Z）的同余子群中的值）的机器到配分函数的直接应用，该配分函数通过编码李代数性质的形式幂级数表示。
英文摘要：
There is a remarkable connection between quantum generating functions of field theory and formal power series associated with dimensions of chains and homologies of suitable Lie algebras. We discuss the homological aspects of this connection with its applications to partition functions of the minimal three-dimensional gravities in the space-time asymptotic to AdS3, which also describe the three-dimensional Euclidean black holes, the pure N = 1 supergravity, and a sigma model on N-fold generalized symmetric products. We also consider in the same context elliptic genera of some supersymmetric sigma models. These examples can be considered as a straightforward application of the machinery of modular forms and spectral functions (with values in the congruence subgroup of SL(2, Z)) to partition functions represented by means of formal power series that encode Lie algebra properties.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
