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Journal of High Energy Physics

, 2018:182 | Cite as

Shockwave S-matrix from Schwarzian quantum mechanics

  • Ho Tat Lam
  • Thomas G. Mertens
  • Gustavo J. Turiaci
  • Herman Verlinde
Open Access
Regular Article - Theoretical Physics

Abstract

Schwarzian quantum mechanics describes the collective IR mode of the SYK model and captures key features of 2D black hole dynamics. Exact results for its correlation functions were obtained in [1]. We compare these results with bulk gravity expectations. We find that the semi-classical limit of the OTO four-point function exactly matches with the scattering amplitude obtained from the Dray-’t Hooft shockwave \( \mathcal{S} \)-matrix. We show that the two point function of heavy operators reduces to the semi-classical saddle-point of the Schwarzian action. We also explain a previously noted match between the OTO four point functions and 2D conformal blocks. Generalizations to higher-point functions are discussed.

Keywords

2D Gravity AdS-CFT Correspondence Black Holes Conformal Field Theory 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Ho Tat Lam
    • 1
  • Thomas G. Mertens
    • 1
    • 3
  • Gustavo J. Turiaci
    • 1
  • Herman Verlinde
    • 1
    • 2
  1. 1.Physics DepartmentPrinceton UniversityPrincetonU.S.A.
  2. 2.Princeton Center for Theoretical SciencePrinceton UniversityPrincetonU.S.A.
  3. 3.Department of Physics and AstronomyGhent UniversityGentBelgium

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