Entanglement Entropy of Quantum Corners

TL;DR

This paper investigates the entanglement entropy associated with quantum corners in 2D gravity, demonstrating that for certain states, the entropy scales with the dilaton, aligning with the semiclassical area law.

Contribution

It introduces a quantum informational framework for corner charges in 2D gravity and derives a formula for entanglement entropy based on quantum corner representation theory.

Findings

Entanglement entropy of semiclassical states scales with the dilaton.

Derived a formula for entanglement entropy from quantum corner representations.

Confirmed the quantum corner entropy aligns with the semiclassical area law.

Abstract

In gravitational theories with boundaries, diffeomorphisms can become physical and acquire a non-vanishing Noether charge. Using the covariant phase space formalism, on shell of the gravitational constraints, the latter localizes on codimension-$2$ surfaces, the corners. The corner proposal asserts that these charges, and their algebras, must be important ingredients of any quantum gravity theory. In this manuscript, we continue the study of quantum corner symmetries and algebras by computing the entanglement entropy and quantum informational properties of quantum states abiding to the quantum representations of corners in the framework of $2$-dimensional gravity. We do so for two classes of states: the vacuum and coherent states, properly defined. We then apply our results to JT gravity, seen as the dimensional reduction of $4$d near extremal black holes. There, we demonstrate that the entanglement entropy of some coherent quantum gravity states -- states admitting a semiclassical description -- scales like the dilaton, reproducing the semiclassical area law behavior and further solidifying the quantum informational nature of entropy of quantum corners. We then study general states and their gluing procedure, finding a formula for the entanglement entropy based entirely on the representation theory of $2$d quantum corners.