Abstract
The authors find constrained instantons -- configurations that extremize the action subject to a constraint -- in Einstein gravity with and without a cosmological constant. Such instantons are expected to contribute to non-perturbative processes in quantum gravity. With negative cosmological constant, these configurations describe wormholes connecting two asymptotic regions.
Highlights
There has been renewed interest in wormholes stemming from recent progress in low-dimensional quantum gravity
Relevant for the anti–de Sitter (AdS)=CFT correspondence, we found explicit solutions corresponding to Euclidean wormholes with a variety of boundary topologies
They may give the dominant contribution from two-sided wormholes with trivial bulk topology in pure quantum gravity
Summary
There has been renewed interest in wormholes stemming from recent progress in low-dimensional quantum gravity. Euclidean wormholes in Jackiw-Teitelboim (JT) and pure 3D anti–de Sitter (AdS) quantum gravity encode the energy level statistics of black hole microstates in those simple models [1,2,3,4]. Assuming perturbative stability in general, we suggest that the one-loop approximation to the path integral over these instantons (including an integral over the instanton parameters) describes a coarse-grained approximation to the energy level statistics of AdS black hole microstates. In this sense, Euclidean quantum gravity would provide a statistically averaged, “mesoscopic” description of microstates
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