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  • Open Access

Nonperturbative toolkit for quantum gravity

Vijay Balasubramanian1,2,3,* and Tom Yildirim4,†

  • *Contact author: vijay@physics.upenn.edu
  • †Contact author: tom.yildirim@physics.ox.ac.uk
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Phys. Rev. D 114, 026035 – Published 27 July, 2026

DOI: https://doi.org/10.1103/nlzj-w34h

Abstract

We propose a method for demonstrating equivalences beyond the saddle point approximation between quantities in quantum gravity that are defined by the Euclidean path integral, without assumptions about holographic duality. The method involves three ingredients: (1) a way of resolving the identity with an overcomplete basis of microstates that is under semiclassical control, (2) a drastic simplification of the sum over topologies in the limit where the basis is infinitely overcomplete, and (3) a way of cutting and splicing geometries to demonstrate equality between two different gravitational path integrals even if neither can be explicitly computed. We illustrate our methods by giving a general argument that the thermal partition function of quantum gravity with two boundaries factorizes. One implication of our results is that universes containing a horizon can sometimes be understood as superpositions of horizonless geometries entangled with a closed universe.

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      Phys. Rev. D 114, 026035– Published 27 July, 2026
      • Received 23 February 2026
      • Accepted 6 July 2026
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      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.

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