标题： 带电AdS引力配分函数的复鞍点 显示英文标题

标题： Complex Saddles of Charged-AdS Gravitational partition function

摘要： 在本文中，我们考虑了(d+1)维带电和不带电AdS黑洞几何的欧几里得配分函数。 可以看出，该配分函数可以简化为一维积分，可以使用Picard-Lefschetz方法进行研究。 系统的鞍点对应于不同参数空间范围内的裸奇点几何、热AdS、小尺寸、中间尺寸或大尺寸黑洞。 这些是爱因斯坦方程的解，在参数空间的不同区域中是主导的鞍点。 对涉及这些鞍点的配分函数的简单分析会导致与黑洞热力学的标准理解以及AdS/CFT的冲突。 然而，当使用Picard-Lefschetz分析配分函数时，可以看出裸奇点几何不会产生贡献。 它们对应的鞍点是无关的，这与宇宙审查假说一致。 对应于负比热的鞍点是小尺寸或中间尺寸的黑洞。 尽管它们在配分函数中是相关的，但属于次主导的。 它们在同调平均下也会消失。 只有对应于非负比热的鞍点才会对欧几里得配分函数产生贡献。 最后，我们使用KSW准则分析了这些复几何的允许性。 显示英文摘要

摘要： In this paper, we consider the Euclidean partition function of charged and uncharged AdS black hole geometries in (d+1)-dimensions. It is seen that the partition function can be reduced to a one-dimensional integral, which can be investigated using methods of Picard-Lefschetz. The saddles of the system correspond to either naked-singular geometry, thermal-AdS, small-, intermediate- or large-sized black hole for different ranges of parameter space. These are solutions of Einstein's equation, which are dominant saddles in the partition function in various regimes of parameter space. A naive analysis of the partition function involving these saddles would lead to conflicts with the standard understanding of black hole thermodynamics and also with AdS/CFT. However, when the partition function is analysed using Picard-Lefschetz, it is seen that naked-singular geometries don't contribute. The saddles corresponding to them are irrelevant, aligning well with the Cosmic Censorship hypothesis. Saddles corresponding to negative specific heat are either small- or intermediate-sized black holes. Although they are relevant in the partition function but are sub-dominant. They also drop out under homology averaging. Saddles corresponding to only non-negative specific heat contribute to the Euclidean partition function. Finally, we analyze the allowability of these complex geometries using the KSW criterion.