Quantum Gravity, Tensor Network, and Holographic Entanglement Entropy
Muxin Han, Florida Atlantic University
The relation between nonperturbative Quantum Gravity and tensor network is explored from the perspectives of bulk-boundary duality and holographic entanglement entropy. We find that the quantum gravity states in a space Σ with boundary ∂Σ is an exact holographic mapping. The tensor network, understood as the boundary quantum state, is the output of the exact holographic mapping emerging from a coarse graining procedure of quantum gravity state. Furthermore, when a region A and its complement are specified on the boundary ∂Σ, 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 ∂Σ.