论文标题
没有共形因子问题的引力热力学：洛伦兹路径积分的分区功能和欧几里得马鞍
Gravitational thermodynamics without the conformal factor problem: Partition functions and Euclidean saddles from Lorentzian Path Integrals
论文作者
论文摘要
传统上，使用欧几里得路径积分研究了引力系统的热分区功能。但是在欧几里得签名中，重力作用遇到了保形因子问题，这使得下面无限的动作。这使得将欧几里得的表述作为基本。然而，尽管它们与周期性的假想时间相关，但热重力分区函数也可以通过实时路径积分来描述，而实际洛伦兹指标定义的轮廓。一个警告是，我们应该允许某些类似于熟悉的欧几里得圆锥形奇异性的Codimension-2奇异性。有了这种理解，我们表明通常的欧几里得 - 签名黑洞（或它们的复杂旋转类似物）定义了计算我们分区功能的实时路径积分的鞍点。此外，当黑孔具有正比热时，我们提供了证据表明，我们的真实洛伦兹 - 签名集成轮廓的Codimension-2子字节可能会变形，以表明这些黑洞鞍座对半经典限制有非零的重量，然后将其余两个整体的整体组成。
Thermal partition functions for gravitational systems have traditionally been studied using Euclidean path integrals. But in Euclidean signature the gravitational action suffers from the conformal factor problem, which renders the action unbounded below. This makes it difficult to take the Euclidean formulation as fundamental. However, despite their familiar association with periodic imaginary time, thermal gravitational partition functions can also be described by real-time path integrals over contours defined by real Lorentzian metrics. The one caveat is that we should allow certain codimension-2 singularities analogous to the familiar Euclidean conical singularities. With this understanding, we show that the usual Euclidean-signature black holes (or their complex rotating analogues) define saddle points for the real-time path integrals that compute our partition functions. Furthermore, when the black holes have positive specific heat, we provide evidence that a codimension-2 subcontour of our real Lorentz-signature contour of integration can be deformed so as to show that these black holes saddles contribute with non-zero weight to the semiclassical limit, and that the same is then true of the remaining two integrals.
