Entanglement Entropy in Loop Quantum Gravity

TL;DR

This paper demonstrates how to define and compute entanglement entropy within loop quantum gravity, linking it to black hole entropy and providing a new approach to study quantum corrections to gravity.

Contribution

It introduces a method to calculate entanglement entropy for spin network states in loop quantum gravity and connects it with the isolated horizon framework.

Findings

Entanglement entropy expressed as sum over boundary punctures

Asymptotic agreement with isolated horizon results

Proposes a new method for quantum corrections to the area law

Abstract

The entanglement entropy between quantum fields inside and outside a black hole horizon is a promising candidate for the microscopic origin of black hole entropy. We show that the entanglement entropy may be defined in loop quantum gravity, and compute its value for spin network states. The entanglement entropy for an arbitrary region of space is expressed as a sum over punctures where the spin network intersects the region's boundary. Our result agrees asymptotically with results previously obtained from the isolated horizon framework, and we give a justification for this agreement. We conclude by proposing a new method for studying corrections to the area law and its implications for quantum corrections to the gravitational action.