JT gravity from partial reduction and defect extremal surface

A bstract We propose the three-dimensional counterpart for Jackiw-Teitelboim gravity coupled with CFT 2 bath based on partial reduction. The is classical AdS a defect brane which has small fluctuation in transverse direction. derive full action by considering as dilaton field. demonstrate that fine-grained entropy computed from island formula precisely agrees extremal surface. Our construction provides Lorentzian higher dimensional glued to and therefore offers framework study problems such black hole information paradox.