JT gravity from partial reduction and defect extremal surface

Abstract

We propose the three-dimensional counterpart for Jackiw-Teitelboim gravity coupled with CFT2 bath based on partial reduction. The three-dimensional counterpart is classical AdS gravity with a defect brane which has small fluctuation in transverse direction. We derive full Jackiw-Teitelboim gravity action by considering the transverse fluctuation as a dilaton field. We demonstrate that the fine-grained entropy computed from island formula precisely agrees with that computed from defect extremal surface. Our construction provides a Lorentzian higher dimensional counterpart for Jackiw-Teitelboim gravity glued to a bath and therefore offers a framework to study problems such as black hole information paradox.