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.

中文翻译：

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复杂性几何和 Schwarzian 动力学

类 SYK 模型的一个著名特征是，在低能量下，它们的动力学降低到单个变量的动力学。在许多设置中，这个“Schwarzian”变量可以解释为双黑洞的极值体积，由此产生的动力学只是指数势中的一维牛顿粒子的动力学。在复杂性方面，尼尔森复杂性几何的简化版本上的测地线在角动量势垒给定的势中也表现得像一维粒子。体积和复杂性的有效作用之间的一致性简洁地总结了各种证据，表明复杂性与黑洞的动力学密切相关。