Entanglement Dynamics in 2D CFT with Boundary: Entropic origin of JT gravity and Schwarzian QM

TL;DR

This work analyzes entanglement dynamics in a 2D CFT with a boundary and shows that the entanglement data alone reproduce gravity-like dynamics, specifically JT dilaton gravity and Schwarzian QM, without assuming a gravitational action. By decomposing the entanglement entropy into a vacuum piece $S_0$ and a subleading piece $S_1=\langle K\rangle$, the authors derive JT equations from entanglement and identify $S_1$ with the dilaton while $S_0$ sets a constant-curvature background via a Liouville-type equation. They further derive the boundary trajectory $\tau(t)$ as a Schwarzian QM degree of freedom, obtaining a Schwarzian action with coupling $C=\frac{c\epsilon}{12\pi}$ through both entropy-based RG arguments and energy-momentum conservation (including Unruh recoil). Finite-temperature analysis reproduces Schwarzian thermodynamics and supports the interpretation of Schwarzian QM as the effective boundary theory of a large-$c$ 2D CFT with a boundary. These results strengthen the view that gravitational dynamics can emerge from pure entanglement structure in quantum field theories.

Abstract

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.

Figures (2)

• Figure 1: The interval labeled by $(u,v)$ (horizontal green line) and its complement (horizontal red line) and the corresponding modular flow (indicated in blue).
• Figure 2: We assume that the boundary layer has a finite effective thickness $\epsilon$, as indicated by the blue dashed line.