Partition Function for a Volume of Space,Physical Review Letters

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Partition Function for a Volume of Space
Physical Review Letters ( IF 8.1 ) Pub Date : 2023-05-31 , DOI: 10.1103/physrevlett.130.221501
Ted Jacobson _{1,

2} , Manus R Visser ₂

Affiliation

We consider the quantum gravity partition function that counts the dimension of the Hilbert space of a spatial region with topology of a ball and fixed proper volume, and evaluate it in the leading order saddle point approximation. The result is the exponential of the Bekenstein-Hawking entropy associated with the area of the saddle ball boundary, and is reliable within effective field theory provided the mild curvature singularity at the ball boundary is regulated by higher curvature terms. This generalizes the classic Gibbons-Hawking computation of the de Sitter entropy for the case of positive cosmological constant and unconstrained volume, and hence exhibits the holographic nature of nonperturbative quantum gravity in generic finite volumes of space.

中文翻译：

空间体积的配分函数

我们考虑量子引力配分函数，该函数计算具有球拓扑和固定固有体积的空间区域的希尔伯特空间的维数，并以前导鞍点近似对其进行评估。结果是与鞍球边界面积相关的贝肯斯坦-霍金熵的指数，并且在有效场理论中是可靠的，前提是球边界处的温和曲率奇点由更高的曲率项调节。这概括了正宇宙常数和无约束体积情况下德西特熵的经典吉本斯-霍金计算，因此展示了一般有限体积空间中非微扰量子引力的全息性质。

更新日期：2023-06-01

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