Membrane theory of entanglement dynamics from holography

TL;DR

This paper demonstrates that a membrane theory describing entanglement dynamics in chaotic systems applies to holographic theories, unifying different approaches and supporting its broad relevance.

Contribution

It reformulates holographic entanglement entropy dynamics within the membrane theory framework, extending its applicability to all chaotic systems.

Findings

Supports membrane theory as a universal description of entanglement dynamics

Reformulates holographic entanglement entropy in membrane terms

Provides evidence linking holography and chaotic system dynamics

Abstract

Recently, a minimal membrane description of the entanglement dynamics of large regions in generic chaotic systems was conjectured in arXiv:1803.00089. Analytic results in random circuits and spin chain numerics support this theory. We show that the results found by the author in arXiv:1612.00082 about the dynamics of entanglement entropy in theories with a holographic dual can be reformulated in terms of the same minimal membrane, providing strong evidence that the membrane theory describes all chaotic systems. We discuss the implications of our results for tensor network approaches to holography and the holographic renormalization group.