Wormhole calculus, replicas, and entropies
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Springer
Received: July 7, 2020 Accepted: August 27, 2020 Published: September 30, 2020
Steven B. Giddings and Gustavo J. Turiaci Department of Physics, University of California, Santa Barbara, CA 93106, U.S.A.
E-mail: [email protected], [email protected] Abstract: We investigate contributions of spacetime wormholes, describing baby universe emission and absorption, to calculations of entropies and correlation functions, for example those based on the replica method. We find that the rules of the “wormhole calculus”, developed in the 1980s, together with standard quantum mechanical prescriptions for computing entropies and correlators, imply definite rules for limited patterns of connection between replica factors in simple calculations. These results stand in contrast with assumptions that all topologies connecting replicas should be summed over, and call into question the explanation for the latter. In a “free” approximation baby universes introduce probability distributions for coupling constants, and we review and extend arguments that successive experiments in a “parent” universe increasingly precisely fix such couplings, resulting in ultimately pure evolution. Once this has happened, the nontrivial question remains of how topology-changing effects can modify the standard description of black hole information loss. Keywords: Black Holes, Gauge-gravity correspondence, Nonperturbative Effects ArXiv ePrint: 2004.02900
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP09(2020)194
JHEP09(2020)194
Wormhole calculus, replicas, and entropies
Contents 1
2 Review of the wormhole calculus
2
3 Renyis, replicas, and wormhole connections 3.1 Entropies 3.2 Correlators
4 5 8
4 Determination of wormhole-induced couplings
9
5 Discussion and lessons
11
A Puzzles for replica wormholes
12
1
Introduction
Nontrivial spacetime topologies, and in particular change in the topology of space, have long been considered to be a possible feature of dynamical gravity. Topology-changing processes were particularly intensively studied in the late 1980s, in the context of the question of their contribution to possible loss of quantum coherence [1–5]. Specifically, one can consider processes where space branches into two disconnected components; one of these may typically be comparatively small, and was called a “baby universe” (BU). In the “free BU” approximation where multiple BUs can be emitted, or rejoin, a bigger “parent universe”, but where the BUs don’t interact or create other large universes, it was found that the leading effect of such processes is not to induce an ongoing loss of quantum coherence [4, 5].1 Instead, these processes lead to an effective probability distribution for coupling constants that multiply operators describing the effect of the BUs on the fields in the parent universe. There has been a recent resurgence of interest in topology change, arising from suggestions that nontrivial topologies may help explain how black hole evolution can be reconciled with unitary q
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