论文标题
Schwarzian在拉伸地平线上的动作注释
A note on the action with the Schwarzian at the stretched horizon
论文作者
论文摘要
在本文中，我们讨论了最近出现的有趣模型的量化。它显示了一种将自由度的边界度与固定非超级黑洞的伸展的地平线相关联的方法，就像在JT重力中对近超级黑洞所做的那样。现在，路径积分包含在自由度的边界程度上的积分，这是拉伸范围的时间重新分析，以保持其长度固定。这些边界的自由度可以看作是$ diff（s^1）/s^1 $的元素，这是在Virasoro组的作用下，这是普通共同连接矢量的共同轨道。从该歧管上的符号形式，我们在边界路径积分中获得了度量。对经典解决方案进行单循环计算，我们发现单循环的答案不是有限的，表明经典解决方案是不稳定的，或者此动作的不确定问题，类似于量子重力中的共形模式问题。通过分析继续该领域，我们获得的边界分区函数与反向温度无关，并且至少在一环下没有促进热力学。这与JT重力中近超级黑洞的研究相反，在该研究中，对热力学的全部贡献来自自由度的边界程度。
In this paper, we discuss the quantization of an interesting model of Carlip which appeared recently. It shows a way to associate boundary degrees of freedom to the stretched horizon of a stationary non-extremal black hole, as has been done in JT gravity for near-extremal black holes. The path integral now contains an integral over the boundary degrees of freedom, which are time reparametrizations of the stretched horizon keeping its length fixed. These boundary degrees of freedom can be viewed as elements of $Diff(S^1)/S^1$, which is the coadjoint orbit of an ordinary coadjoint vector under the action of the Virasoro group. From the symplectic form on this manifold, we obtain the measure in the boundary path integral. Doing a one-loop computation about the classical solution, we find that the one-loop answer is not finite, signalling that either the classical solution is unstable or there is an indefiniteness problem with this action, similar to the conformal mode problem in quantum gravity. Upon analytically continuing the field, the boundary partition function we get is independent of the inverse temperature and does not contribute to the thermodynamics at least at one-loop. This is in contrast to the study of near-extremal black holes in JT gravity, where the entire contribution to thermodynamics is from boundary degrees of freedom.
