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 ϵ and constant boundary entropy, we derive that its location satisfies the equations of motion of Schwarzian quantum mechanics with coupling constant C = c ϵ/12π. We rederive this result via energy-momentum conservation.
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics
- 2D Gravity
- ArXiv ePrint: 1808.05583
- Conformal Field Theory
- Field Theories in Lower Dimensions