For quantum gravity states associated to open spin network graphs, we study how the boundary (the set of open edges, which carries spin degrees of freedom) is affected by the bulk, specifically by its combinatorial structure and by the quantum correlations among the intertwiners. In particular, we determine under which conditions certain classes of quantum gravity states map bulk degrees of freedom into boundary ones isometrically (which is a necessary condition for holography). We then look at the entanglement entropy of the boundary and recover, for slightly entangled intertwiners, the Ryu-Takayanagi formula with corrections induced by the entanglement entropy of the bulk state. We also show that the presence of a region with highly entangled intertwiners deforms the minimal-area surface, which is prevented from entering that region when the entanglement entropy of the latter exceeds a certain bound, a mechanism which thus leads to the rise of a black hole-like region in the bulk.
- Quantum Gravity
- Scientific Series