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

TL;DR

This paper explores how boundary effects influence entanglement entropy in 2D conformal field theories, revealing that their dynamics are governed by equations akin to 2D gravity and Schwarzian quantum mechanics, linking entropic behavior to gravitational models.

Contribution

It demonstrates that boundary-induced entanglement dynamics in 2D CFTs are described by equations similar to 2D JT gravity and Schwarzian QM, providing a new entropic perspective on these gravitational theories.

Findings

Boundary entanglement dynamics follow local equations of motion similar to 2D gravity.

The boundary's position obeys Schwarzian equations with a specific coupling constant.

Re-derivation via energy-momentum conservation confirms the results.

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 $\epsilon$ 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.