Quantum Entanglement on Black Hole Horizons in String Theory and Holography

We compute the exact one-loop partition function of ${\mathbb{Z}}_N$ orbifolds of Euclidean BTZ black hole with the aim to compute the entanglement entropy of the black hole horizon in string theory as a function of the mass and spin of the black hole and the ${\mathrm{A}\mathrm{d}\mathrm{S}}_3$ radius. We analyze the tachyonic contribution to the modular integrand for the partition function known for odd integers $N>1$ and show that it admits an analytic continuation resulting in a finite answer for the modular integral in the physical region $0<N\le 1$. We discuss the flat space limit and the relevance of this computation for quantum gravity near black hole horizons and holography in relation to the thermal entropy.