Topological Entanglement Entropy in Euclidean AdS₃ via Surgery

We calculate the topological entanglement entropy (TEE) in Euclidean asymptotic AdS₃ spacetime using surgery. Bipartiting along the horizon of the eternal BTZ black hole, we get TEE exactly matching the Bekenstein-Hawking entropy, which supports the ER=EPR conjecture in the Euclidean bulk. After summing partition functions over genus-one classical geometries, we compute TEE at high-temperature. In the case with the most negative global curvature, we find that TEE equals that of the Moonshine double state, given by the maximally-entangled superposition of 194 types of “anyons” in the bulk, labeled by irreducible representations of the Monster group. We propose this as the bulk analog of the thermofield double state in the Euclidean AdS₃.