Finite Entanglement Entropy in String Theory

Abstract

We analyze the one-loop quantum entanglement entropy in ten-dimensional Type-II string theory using the orbifold method by analytically continuing in $N$ the genus-one partition function for string orbifolds on $\mathbb{R}^2/\mathbb{Z}_N$ conical spaces known for all odd integers $N > 1$. We show that the tachyonic contributions to the orbifold partition function can be appropriately summed and analytically continued to an expression that is finite in the physical region $0 < N \leq 1$ resulting in a finite and calculable answer for the entanglement entropy. We discuss the implications of the finiteness of the entanglement entropy for the information paradox, quantum gravity, and holography.