Complexity geometry and Schwarzian dynamics

  • Henry W. LinEmail author
  • Leonard Susskind
Open Access
Regular Article - Theoretical Physics


A celebrated feature of SYK-like models is that at low energies, their dynamics reduces to that of a single variable. In many setups, this “Schwarzian” variable can be interpreted as the extremal volume of the dual black hole, and the resulting dynamics is simply that of a 1D Newtonian particle in an exponential potential. On the complexity side, geodesics on a simplified version of Nielsen’s complexity geometry also behave like a 1D particle in a potential given by the angular momentum barrier. The agreement between the effective actions of volume and complexity succinctly summarizes various strands of evidence that complexity is closely related to the dynamics of black holes.


2D Gravity AdS-CFT Correspondence 


Open Access

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Copyright information

© The Author(s) 2020

Authors and Affiliations

  1. 1.Jadwin HallPrinceton UniversityPrincetonUSA
  2. 2.Stanford Institute for Theoretical Physics and Department of PhysicsStanford UniversityStanfordUSA
  3. 3.GoogleMountain ViewUSA

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