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  • Letter
  • Open Access

Partition function of a volume of space in a higher curvature theory

Aydin Tavlayan* and Bayram Tekin†

  • Department of Physics, Middle East Technical University, 06800 Ankara, Turkey

  • *aydint@metu.edu.tr
  • †btekin@metu.edu.tr
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Phys. Rev. D 108, L041902 – Published 28 August, 2023

DOI: https://doi.org/10.1103/PhysRevD.108.L041902

Abstract

Recently, Jacobson and Visser [Partition Function for a Volume of Space, Phys. Rev. Lett. 130, 221501 (2023).] calculated the quantum partition function of a fixed, finite volume of a region with the topology of a ball in the saddle point approximation within the context of Einstein’s gravity with or without a cosmological constant. The result can be interpreted as the dimension of Hilbert space of the theory. Here we extend their computation to a theory defined in principle with infinitely many powers of curvature in three dimensions. We confirm their result: The partition function of a spatial region in the leading saddle point approximation is given as the exponential of the Bekenstein-Hawking or the Wald entropy of the boundary of the finite spatial region both in the case of zero and finite cosmological constant. In the latter case, the effective Newton’s constant appears in the entropy formula. The calculations lend support to the holographic nature of gravity for finite regions of space with a boundary.

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Phys. Rev. D 108, L041902– Published 28 August, 2023
  • Received 28 July 2023
  • Accepted 14 August 2023
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