Chaos in AdS$_2$ holography

TL;DR

The paper argues that AdS$_2$ holography inspired by SYK-like dynamics does not admit a conventional weakly curved gravity dual but can be captured by a novel hydrodynamic action that couples to conformal quantum mechanics correlators. It derives an effective action for gravity near an AdS$_2$ throat, showing that the boundary dynamics are governed by a diffeomorphism (Schwarzian) sector plus a CQM, and uses this to compute four-point functions. The hydrodynamic contribution to the four-point function yields a Lyapunov exponent $\lambda_L = 2\pi T$, saturating the chaos bound and indicating maximal chaos in this setup. Together, these results suggest a universal IR description for large-$N$ emergent conformal quantum systems in two dimensions, with potential gauged SYK/AdS$_2$ connections, rather than a conventional gravity dual.

Abstract

We revisit AdS$_2$ holography with the Sachdev-Ye-Kitaev models in mind. Our main result is to rewrite a generic theory of gravity near an AdS$_2$ throat as a novel hydrodynamics coupled to the correlation functions of a conformal quantum mechanics. This gives a prescription for the computation of $n$-point functions in the dual quantum mechanics. We thereby find that the dual is maximally chaotic.