Loop Quantum Gravity, Exact Holographic Mapping, and Holographic Entanglement Entropy

TL;DR

This paper demonstrates that Loop Quantum Gravity spin-network states can serve as an exact holographic mapping, and that boundary entanglement entropy in this framework obeys the Ryu-Takayanagi formula, linking LQG with holographic entanglement.

Contribution

It establishes a direct connection between LQG spin-networks and holographic duality, showing the emergence of tensor networks and entanglement entropy relations.

Findings

LQG spin-networks form an exact holographic mapping.

Boundary entanglement entropy follows the Ryu-Takayanagi formula.

The tensor network arises from coarse graining of spin-networks.

Abstract

The relation between Loop Quantum Gravity (LQG) and tensor network is explored from the perspectives of bulk-boundary duality and holographic entanglement entropy. We find that the LQG spin-network states in a space $\Sigma$ with boundary $\partial\Sigma$ is an exact holographic mapping similar to the proposal in arXiv:1309.6282. The tensor network, understood as the boundary quantum state, is the output of the exact holographic mapping emerging from a coarse graining procedure of spin-networks. Furthermore, when a region $A$ and its complement $\bar{A}$ are specified on the boundary $\partial\Sigma$, we show that the boundary entanglement entropy $S(A)$ of the emergent tensor network satisfies the Ryu-Takayanagi formula in the semiclassical regime, i.e. $S(A)$ is proportional to the minimal area of the bulk surface attached to the boundary of $A$ in $\partial\Sigma$.