Random matrix theory for complexity growth and black hole interiors
Abstract We study a precise and computationally tractable notion of operator complexity in holographic quantum theories, including the ensemble dual of Jackiw-Teitelboim gravity and two-dimensional holographic conformal field theories. This is a refined, “microc...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Springer Berlin Heidelberg
2022
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| Online Access: | https://hdl.handle.net/1721.1/138851 |
| _version_ | 1826200976886857728 |
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| author | Kar, Arjun Lamprou, Lampros Rozali, Moshe Sully, James |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Kar, Arjun Lamprou, Lampros Rozali, Moshe Sully, James |
| author_sort | Kar, Arjun |
| collection | MIT |
| description | Abstract
We study a precise and computationally tractable notion of operator complexity in holographic quantum theories, including the ensemble dual of Jackiw-Teitelboim gravity and two-dimensional holographic conformal field theories. This is a refined, “microcanonical” version of K-complexity that applies to theories with infinite or continuous spectra (including quantum field theories), and in the holographic theories we study exhibits exponential growth for a scrambling time, followed by linear growth until saturation at a time exponential in the entropy — a behavior that is characteristic of chaos. We show that the linear growth regime implies a universal random matrix description of the operator dynamics after scrambling. Our main tool for establishing this connection is a “complexity renormalization group” framework we develop that allows us to study the effective operator dynamics for different timescales by “integrating out” large K-complexities. In the dual gravity setting, we comment on the empirical match between our version of K-complexity and the maximal volume proposal, and speculate on a connection between the universal random matrix theory dynamics of operator growth after scrambling and the spatial translation symmetry of smooth black hole interiors. |
| first_indexed | 2024-09-23T11:44:22Z |
| format | Article |
| id | mit-1721.1/138851 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:44:22Z |
| publishDate | 2022 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1388512023-12-08T17:08:58Z Random matrix theory for complexity growth and black hole interiors Kar, Arjun Lamprou, Lampros Rozali, Moshe Sully, James Massachusetts Institute of Technology. Center for Theoretical Physics Abstract We study a precise and computationally tractable notion of operator complexity in holographic quantum theories, including the ensemble dual of Jackiw-Teitelboim gravity and two-dimensional holographic conformal field theories. This is a refined, “microcanonical” version of K-complexity that applies to theories with infinite or continuous spectra (including quantum field theories), and in the holographic theories we study exhibits exponential growth for a scrambling time, followed by linear growth until saturation at a time exponential in the entropy — a behavior that is characteristic of chaos. We show that the linear growth regime implies a universal random matrix description of the operator dynamics after scrambling. Our main tool for establishing this connection is a “complexity renormalization group” framework we develop that allows us to study the effective operator dynamics for different timescales by “integrating out” large K-complexities. In the dual gravity setting, we comment on the empirical match between our version of K-complexity and the maximal volume proposal, and speculate on a connection between the universal random matrix theory dynamics of operator growth after scrambling and the spatial translation symmetry of smooth black hole interiors. 2022-01-10T12:52:27Z 2022-01-10T12:52:27Z 2022-01-05 2022-01-09T04:10:00Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/138851 Journal of High Energy Physics. 2022 Jan 05;2022(1):16 PUBLISHER_CC en https://doi.org/10.1007/JHEP01(2022)016 Creative Commons Attribution https://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Kar, Arjun Lamprou, Lampros Rozali, Moshe Sully, James Random matrix theory for complexity growth and black hole interiors |
| title | Random matrix theory for complexity growth and black hole interiors |
| title_full | Random matrix theory for complexity growth and black hole interiors |
| title_fullStr | Random matrix theory for complexity growth and black hole interiors |
| title_full_unstemmed | Random matrix theory for complexity growth and black hole interiors |
| title_short | Random matrix theory for complexity growth and black hole interiors |
| title_sort | random matrix theory for complexity growth and black hole interiors |
| url | https://hdl.handle.net/1721.1/138851 |
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