  We propose the three-dimensional bulk dual for Jackiw-Teitelboim gravity
coupled with CFT$_2$ bath based on partial reduction. The bulk dual 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 dual for Jackiw-Teitelboim gravity and therefore
offers a framework to study problems such as black hole information paradox as
well as gravity/ensemble duality.
