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Partition Function for a Volume of Space

Ted Jacobson and Manus R. Visser
Phys. Rev. Lett. 130, 221501 – Published 31 May 2023
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Abstract

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.

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  • Received 2 March 2023
  • Revised 7 April 2023
  • Accepted 26 April 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.221501

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Ted Jacobson1,2 and Manus R. Visser2

  • 1Maryland Center for Fundamental Physics, University of Maryland, College Park, Maryland 20742, USA
  • 2Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom

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Issue

Vol. 130, Iss. 22 — 2 June 2023

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