Finite Entanglement Entropy in String Compactifications

Atish Dabholkar

I discuss physical motivations from black hole physics and holography for expecting finite quantum entanglement entropy in quantum gravity. I describe recent and earlier results in defining such a notion in perturbative string theory by a stringy analog of the replica method using ZN orbifolds constructed for any odd positive integer N. The entropy so defined naturally includes a classical piece and is manifestly UV finite but has potential tachyonic IR divergences. I show that for several string compactifications, the specific structure of the tachyonic spectrum allows for a re-summation and analytic continuation to the physical region 0 < N ≤ 1 where the IR divergences are absent and the resulting entropy is finite to one-loop order.

https://www.ias.edu/video/finite-entanglement-entropy-string-compactifications