The DOI matches its Crossref record; 40 of the 40 references it cites were found in a registry or an index.
Holographic Complexity Equals Bulk Action?
Open accessAbstract
We conjecture that the quantum complexity of a holographic state is dual to the action of a certain spacetime region that we call a Wheeler-DeWitt patch. We illustrate and test the conjecture in the context of neutral, charged, and rotating black holes in anti-de Sitter spacetime, as well as black holes perturbed with static shells and with shock waves. This conjecture evolved from a previous conjecture that complexity is dual to spatial volume, but appears to be a major improvement over the original. In light of our results, we discuss the hypothesis that black holes are the fastest computers in nature.
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Cites
Susskind, L. (1994) · arXiv · doi:10.48550/arxiv.hep-th/9409089 · Cited by 4,085
Self-citationSusskind, L. (1995) · Journal of Mathematical Physics · doi:10.1063/1.531249 · Cited by 4,085
Self-citationMaldacena, J., Shenker, S. H., & Stanford, D. (2016) · Journal of High Energy Physics · doi:10.1007/jhep08(2016)106 · Cited by 2,313
Black holes and the butterfly effect
Shenker, S. H., & Stanford, D. (2014) · Journal of High Energy Physics · doi:10.1007/jhep03(2014)067 · Cited by 1,533
Black holes as mirrors: quantum information in random subsystems
Hayden, P., & Preskill, J. (2007) · Journal of High Energy Physics · doi:10.1088/1126-6708/2007/09/120 · Cited by 1,332
Hartnoll, S. A., Herzog, C. P., & Horowitz, G. T. (2008) · Journal of High Energy Physics · doi:10.1088/1126-6708/2008/12/015 · Cited by 1,204
Universal upper bound on the entropy-to-energy ratio for bounded systems
Bekenstein, J. D. (1981) · Physical Review D · doi:10.1103/physrevd.23.287 · Cited by 1,182
Ultimate physical limits to computation
Lloyd, S. (2000) · Nature · doi:10.1038/35023282 · Cited by 1,120
Sekino, Y., & Susskind, L. (2008) · Journal of High Energy Physics · doi:10.1088/1126-6708/2008/10/065 · Cited by 1,112
Self-citationDimensional reduction in quantum gravity
Hooft, G. ’. (1993) · Utrecht University Repository (Utrecht University) · Cited by 1,085
Cited by
Complexity, action, and black holes
Brown, A. R., Roberts, D. A., Susskind, L., Swingle, B., & Zhao, Y. (2016) · Physical Review D · doi:10.1103/physrevd.93.086006 · Cited by 640
Self-citationChaos and complexity by design
Roberts, D. A., & Yoshida, B. (2017) · Journal of High Energy Physics · doi:10.1007/jhep04(2017)121 · Cited by 455
Self-citationSecond law of quantum complexity
Brown, A. R., & Susskind, L. (2018) · Physical Review D · doi:10.1103/physrevd.97.086015 · Cited by 292
Self-citationComments on holographic complexity
Carmi, D., Myers, R. C., & Rath, P. (2017) · Journal of High Energy Physics · doi:10.1007/jhep03(2017)118 · Cited by 292
Noether charge, black hole volume, and complexity
Couch, J., Fischler, W., & Nguyen, P. H. (2017) · Journal of High Energy Physics · doi:10.1007/jhep03(2017)119 · Cited by 257
Metadata
- Authors
- Brown, A. R., Roberts, D. A., Susskind, L., Swingle, B., & Zhao, Y.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2016-05-09
- Volume
- 116
- Issue
- 19
- Pages
- 191301-191301
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2203723895
- Cited by
- 852
- References
- 40
- FWCI
- 48.01
- Type
- journal article
- Language
- en
- Open access
- bronze
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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