Membrane theory of entanglement dynamics from holography

Recently, a minimal membrane description of the entanglement dynamics of large regions in generic chaotic systems was conjectured in Jonay, Huse, and Nahum (arXiv: 1803.00089). Analytic results in random circuits and spin chain numerics support this theory. We show that the results found by Mezei [J. High Energy Phys. 05 (2017) 064], 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.