Holographic Order from Modular Chaos

TL;DR

The paper addresses how chaos in modular flow encodes emergent bulk geometry in holography, deriving a precise bound on exponential growth with exponent $2\pi$ for matrix elements of $\delta H_\text{mod}$ under modular time. It introduces modular scrambling modes that saturate the bound and, via the JLMS relation, map to local null shifts of the bulk RT surface, acting as approximate isometries near the surface. The algebra of these scrambling modes reproduces the local bulk Poincaré algebra and, through their commutator, connects to bulk curvature and modular Berry holonomies. Together, these results provide a framework tying entanglement structure to emergent gravity and suggest links to operator size and effective light-ray theories near entanglement horizons.

Abstract

We argue for an exponential bound characterizing the chaotic properties of modular Hamiltonian flow of QFT subsystems. In holographic theories, maximal modular chaos is reflected in the local Poincare symmetry about a Ryu-Takayanagi surface. Generators of null deformations of the bulk extremal surface map to modular scrambling modes -positive CFT operators saturating the bound- and their algebra probes the bulk Riemann curvature, clarifying the modular Berry curvature proposal of arXiv:1903.04493.