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Probabilistic deconstruction of a theory of gravity, Part I: flat space
by S. Josephine Suh
This Submission thread is now published as
|Authors (as registered SciPost users):||Josephine Suh|
|Preprint Link:||https://arxiv.org/abs/2108.10916v3 (pdf)|
|Date submitted:||2023-08-17 04:08|
|Submitted by:||Suh, Josephine|
|Submitted to:||SciPost Physics|
We define and analyze a stochastic process in anti-de Sitter Jackiw-Teitelboim gravity, induced by the quantum dynamics of the boundary and whose random variable takes values in $AdS_2$. With the boundary in a thermal state and for appropriate parameters, we take the asymptotic limit of the quantum process at short time scales and flat space, and show associated classical joint distributions have the Markov property. We find that Einstein's equations of the theory, sans the cosmological constant term, arise in the semi-classical limit of the quantum evolution of probability under the asymptotic process. In particular, in flat Jackiw-Teitelboim gravity, the area of compactified space solved for by Einstein's equations can be identified as a probability density evolving under the Markovian process.
Published as SciPost Phys. 15, 174 (2023)
Author comments upon resubmission
I have composed replies to both of the referee's reports, answering their questions, and have resubmitted a revised version of the manuscript that includes additional exposition as appropriate.
List of changes
The new Conclusion and Discussion section includes an exposition of
1. the role that the microscopic SYK model plays in our discussion
2. how the bulk spacetime AdS_2 emerges and our new proposal regarding the emergent spacetime
2. the role of Dirichlet b.c. and negative cosmological constant in the JT action
3. relation to previous research deriving Einstein's equations from entanglement entropy.
Submission & Refereeing History
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- Report 2 submitted on 2023-09-14 00:17 by Anonymous
- Report 1 submitted on 2023-09-09 04:15 by Anonymous