SciPost Submission Page
Random Circuits in the Black Hole Interior
by Javier M. Magan, Martin Sasieta, Brian Swingle
Submission summary
| Authors (as registered SciPost users): | Martin Sasieta |
| Submission information | |
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| Preprint Link: | scipost_202506_00012v1 (pdf) |
| Date accepted: | June 16, 2025 |
| Date submitted: | June 5, 2025, 3 p.m. |
| Submitted by: | Martin Sasieta |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
In this paper, we present a quantitative holographic relation between a microscopic measure of randomness and the geometric length of the wormhole in the black hole interior. To this end, we perturb an AdS black hole with Brownian semiclassical sources, implementing the continuous version of a random quantum circuit for the black hole. We use the random circuit to prepare ensembles of states of the black hole whose semiclassical duals contain Einstein-Rosen (ER) caterpillars: long cylindrical wormholes with large numbers of matter inhomogeneities, of linearly growing length with the circuit time. In this setup, we show semiclassically that the ensemble of ER caterpillars of average length $k\ell_{\Delta}$ and matter correlation scale $\ell_{\Delta}$ forms an approximate quantum state $k$-design of the black hole. At exponentially long circuit times, the ensemble of ER caterpillars becomes polynomial-copy indistinguishable from a collection of random states of the black hole. We comment on the implications of these results for holographic circuit complexity and for the holographic description of the black hole interior.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
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- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
List of changes
Added a clarification of the classical matter outside of the black hole in the caption of Fig. 6.
Modified the caption of Fig. 6 to correct that $\exp(-\tau H_{\text{eff},1})|{\text{TFD}}\rangle$ is the Euclidean evolution of a state.
Added footnote 11 to clarify how it is possible to take $K \sim N^2$ perturbations in AdS/CFT without leaving the supergravity regime.
Above Eq. (2.21) we have clarified that the Lorentzian eternal traversable wormhole relies on the exact isometry being present in the Euclidean section.
Expanded Sec. 3.5 to include the role of the logarithmic corrections to the scaling. We have made more transparent that we are using a leading asymptotic form of this relation in the introduction and conclusions. We have improved the presentation of the relation in the introduction and conclusions accordingly.
In footnote 14 we added a comment comparing the average geometry with the setup of Fig. 7 of Ref. [14].
Improved Fig. 1 replacing the hand-drawn figure by a numerical simulation of the exponentially decaying correlations of the ER caterpillar.
Slightly modified Fig. 24.
Added references.
Published as SciPost Phys. 19, 007 (2025)
Reports on this Submission
Strengths
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Papers explores the black hole interior, which is an important open question in holography.
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Very well written.
Weaknesses
Report
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)