Holographic Order from Modular Chaos
Jan de Boer, Lampros Lamprou
TL;DR
This paper explores the chaotic behavior of modular Hamiltonian flow in quantum field theories, revealing a bound linked to holographic duality and connecting bulk geometry with boundary operators.
Contribution
It introduces an exponential bound on modular chaos and relates modular scrambling modes to bulk Riemann curvature in holographic theories.
Findings
Maximal modular chaos corresponds to local Poincare symmetry near Ryu-Takayanagi surfaces.
Modular scrambling modes saturate the chaos bound and probe bulk curvature.
The algebra of modular modes clarifies the modular Berry curvature in holography.
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.
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