  We study the dynamics of the geometric entanglement entropy of a 2D CFT in
the presence of a boundary. We show that this dynamics is governed by local
equations of motion, that take the same form as 2D Jackiw-Teitelboim gravity
coupled to the CFT. If we assume that the boundary has a small thickness
$\epsilon$ and constant boundary entropy, we derive that its location satisfies
the equations of motion of Schwarzian quantum mechanics with coupling constant
$C = {c \epsilon}/{12\pi}$. We rederive this result via energy-momentum
conservation.

High Energy Physics - Theory