The DOI matches its Crossref record; 72 of the 73 references it cites were found in a registry or an index.
Stringy effects in scrambling
Open accessAbstract
In [1] we gave a precise holographic calculation of chaos at the scrambling time scale. We studied the influence of a small perturbation, long in the past, on a two-sided correlation function in the thermofield double state. A similar analysis applies to squared commutators and other out-of-time-order one-sided correlators [2-6]. The essential bulk physics is a high energy scattering problem near the horizon of an AdS black hole. The above papers used Einstein gravity to study this problem; in the present paper we consider stringy and Planckian corrections. Elastic stringy corrections play an important role, effectively weakening and smearing out the development of chaos. We discuss their signature in the boundary field theory, commenting on the extension to weak coupling. Inelastic effects, although important for the evolution of the state, leave a parametrically small imprint on the correlators that we study. We briefly discuss ways to diagnose these small corrections, and we propose another correlator where inelastic effects are order one.
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In the citing paper
“In the context of semi-classical AdS/CFT, the OTOC is computed in gravity by a four-point function in a black hole background as shown in Fig. 12, see Shenker and Stanford (2015) for a detailed explanation.”
From Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity (2023) · cites this paper as Shenker and Stanford (2015)
In the citing paper
“In this basis the S-matrix should be the Dray–‘t Hooft shockwave S-matrix , where and are the Kruskal momenta of the two particles being scattered. Applying the change of basis between the Dray–‘t Hooft S-matrix from Kruskal to Schwarschild energies, which can be found in Shenker and Stanford (2015), gives the expression:3.44”
From Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity (2023) · cites this paper as Shenker and Stanford (2015)
Citations
Cites
Eternal black holes in anti-de Sitter
Maldacena, J. (2003) · Journal of High Energy Physics · doi:10.1088/1126-6708/2003/04/021 · Cited by 1,555
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
Self-citationBlack Holes: Complementarity or Firewalls?
Almheiri, A., Marolf, D., Polchinski, J., & Sully, J. (2012) · arXiv · doi:10.48550/arxiv.1207.3123 · Cited by 1,471
Black holes: complementarity or firewalls?
Almheiri, A., Marolf, D., Polchinski, J., & Sully, J. (2013) · Journal of High Energy Physics · doi:10.1007/jhep02(2013)062 · Cited by 1,470
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
Sekino, Y., & Susskind, L. (2008) · Journal of High Energy Physics · doi:10.1088/1126-6708/2008/10/065 · Cited by 1,112
Black holes: Complementarity or firewalls?
Almheiri, A., Marolf, D., Polchinski, J., & Sully, J. (2013) · eScholarship (California Digital Library) · Cited by 978
Conformal collider physics: energy and charge correlations
A, D. M. H., & Maldacena, J. (2008) · Journal of High Energy Physics · doi:10.1088/1126-6708/2008/05/012 · Cited by 826
Strings in AdS3 and the SL(2,R) WZW model. I: The spectrum
MALDACENA, J. M., & Ooguri, H. (2001) · Journal of Mathematical Physics · doi:10.1063/1.1377273 · Cited by 732
Exact and approximate unitary 2-designs and their application to fidelity estimation
Dankert, C., Cleve, R., Emerson, J., & Livine, E. R. (2009) · Physical Review A · doi:10.1103/physreva.80.012304 · Cited by 683
Research works printed but not linked: 4
- B. Freivogel and L. Susskind, A Framework for the landscape, Phys. Rev. D 70 (2004) 126007 [ hep-th/0408133 ] [ INSPIRE ]. · arXiv
- D.A. Roberts and D. Stanford, Two-dimensional conformal field theory and the butterfly effect, arXiv:1412.5123 [ INSPIRE ]. · arXiv
- J. de Boer, H. Ooguri, H. Robins and J. Tannenhauser, String theory on AdS 3, JHEP 12 (1998) 026 [ hep-th/9812046 ] [ INSPIRE ]. · arXiv
- J.M. Maldacena and H. Ooguri, Strings in AdS 3 and the S L 2 ℝ $$ \mathrm{S}\mathrm{L}\left(2,\mathbb{R}\right) $$ WZW model. Part 3. Correlation functions, Phys. Rev. D 65 (2002) 106006 [ hep-th/0111180 ] [ INSPIRE ]. · arXiv
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Sorted by citations
MALDACENA, J. M., Shenker, S. H., & Stanford, D. (2016) · Journal of High Energy Physics · doi:10.1007/jhep08(2016)106 · Cited by 2,287
Self-citationRemarks on the Sachdev-Ye-Kitaev model
Maldacena, J., & Stanford, D. (2016) · Physical Review D · doi:10.1103/physrevd.94.106002 · Cited by 1,852
Self-citationConformal symmetry and its breaking in two-dimensional nearly anti-de Sitter space
Maldacena, J., Stanford, D., & Yang, Z. (2016) · Progress of Theoretical and Experimental Physics · doi:10.1093/ptep/ptw124 · Cited by 1,068
Self-citationHolographic Complexity Equals Bulk Action?
Brown, A. R., Roberts, D. A., Susskind, L., Swingle, B. G., & Zhao, Y. (2016) · Physical Review Letters · doi:10.1103/physrevlett.116.191301 · Cited by 830
Operator Spreading in Random Unitary Circuits
Nahum, A., Vijay, S., & Haah, J. (2018) · Physical Review X · doi:10.1103/physrevx.8.021014 · Cited by 791
Metadata
- Authors
- Shenker, S. H., & Stanford, D.
- Affiliations
- Stanford University (US)
- Institute for Advanced Study (US)
- Corresponding author
- Stanford, Douglas
- Venue
- Journal of High Energy Physics
- Published
- 2015-05
- Volume
- 2015
- Issue
- 5
- ISSN
- 1029-8479 (ISSN-L)
- OpenAlex
- W1744159570
- Cited by
- 604
- References
- 73
- Citations by year
- 2026: 22 · 2025: 42 · 2024: 54 · 2023: 69 · 2022: 61 · 2021: 72 · 2020: 53 · 2019: 70 · 2018: 66 · 2017: 53 · 2016: 32 · 2015: 10
- FWCI
- 26.88
- Type
- journal article
- Language
- en
- Open access
- diamond
- doi.org
- Licence
- cc-by
- Locations
- Journal of High Energy Physics (publishedVersion, cc-by)
- Funders
- National Science Foundation (1066293, 1314311, PHY-131-4311, 1316699)
- John Templeton Foundation
- Aspen Center for Physics (1066293, PHYS-1066293)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Quantum chaos and dynamical systems
- Keywords
- quantum chaos, scrambling, thermofield double state, out-of-time-order correlators, AdS black holes, string corrections, inelastic behavior, elastic scattering, weak coupling
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