Journal of High Energy Physics

, 2019:75 | Cite as

On the relation between the magnitude and exponent of OTOCs

  • Yingfei GuEmail author
  • Alexei Kitaev
Open Access
Regular Article - Theoretical Physics


We derive an identity relating the growth exponent of early-time OTOCs, the pre-exponential factor, and a third number called “branching time”. The latter is defined within the dynamical mean-field framework, namely, in terms of the retarded kernel. This identity can be used to calculate stringy effects in the SYK and similar models; we also explicitly define “strings” in this context. As another application, we consider an SYK chain. If the coupling strength βJ is above a certain threshold and nonlinear (in the magnitude of OTOCs) effects are ignored, the exponent in the butterfly wavefront is exactly 2π/β.


AdS-CFT Correspondence 1/N Expansion Models of Quantum Gravity 


Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Harvard UniversityCambridgeU.S.A.
  2. 2.California Institute of TechnologyPasadenaU.S.A.

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