Stringy effects in scrambling
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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 context of semi-classical AdS/CFT, the OTOC is computed in gravity by a four-point function in a black hole background.
“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 Kruskal basis, the S-matrix is the Dray-'t Hooft shockwave S-matrix.
“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)
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- 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 › Statistical and Nonlinear 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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