论文标题
在波动球上的2D量子重力分区功能
2D quantum gravity partition function on the fluctuating sphere
论文作者
论文摘要
在最近关于2D量子重力与列乌维尔理论之间的联系的著作中，我们重新审视了后者并阐明了其分区函数的计算的某些方面：我们在中心电荷有限值下对Liouville分区函数的详细计算进行了详细计算。给出了跨理论和定时理论的结果，并分析了它们的性质。我们讨论了从dozz公式的分区函数的推导，其使用库仑气体方法的推导，使用固定区域鞍点对其进行了半经典计算，最后，我们得出了与及时分区函数的精确表达，其扩展可以与文献中报道的3循环触发计算进行比较。我们还讨论了与2D黑洞和其他相关主题的联系。
Motivated by recent works on the connection between 2D quantum gravity and timelike Liouville theory, we revisit the latter and clarify some aspects of the computation of its partition function: We present a detailed computation of the Liouville partition function on the fluctuating sphere at finite values of the central charge. The results for both the spacelike theory and the timelike theory are given, and their properties analyzed. We discuss the derivation of the partition function from the DOZZ formula, its derivation using the Coulomb gas approach, a semiclassical computation of it using the fixed area saddle point, and, finally, we arrive to an exact expression for the timelike partition function whose expansion can be compared with the 3-loop perturbative calculations reported in the literature. We also discuss the connection to the 2D black hole and other related topics.
