Black Hole Entropy from String Entanglement

Abstract: We discuss the notion of string entanglement in string theory, which aims to study entanglement between worldsheet Hilbert spaces rather than entanglement between spacetime Hilbert spaces defined on a time slice in spacetime. Applying this framework to the FZZ duality and its extension to a three-dimensional black hole, we argue that the thermal entropy of 2d and 3d black holes is accounted for by the string entanglement entropy between folded strings arising in the dual sine-Liouville CFT. We compute this via a worldsheet replica method and show that it decomposes into two parts, which we call the vertex operator contribution and the replica contribution. The former can be evaluated analytically and is shown to coincide with the black hole thermal entropies in the low temperature limit in large D dimensions. Although a computation of the latter is left as an open problem, we present evidence that it captures the remaining portion of the black hole entropy.