Complexity geometry and Schwarzian dynamics
Henry W. Lin, Leonard Susskind
Abstract
A bstract 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.
Topics & Concepts
PhysicsDynamics (music)GeodesicClassical mechanicsParticle dynamicsNewtonian dynamicsExponential functionMomentum (technical analysis)Angular momentumNewtonian fluidTheoretical physicsFeature (linguistics)Differential geometryGeometryParticle (ecology)Motion (physics)Statistical physicsBlack hole (networking)Exponential decayInvariant (physics)Volume (thermodynamics)Total angular momentum quantum numberVariable (mathematics)Black Holes and Theoretical PhysicsPulsars and Gravitational Waves ResearchNoncommutative and Quantum Gravity Theories