Notes on Entanglement Entropy in String Theory

TL;DR

This paper investigates entanglement entropy in string theory, deriving a new formula for free higher spin fields and demonstrating UV finiteness of entanglement entropy in closed superstring due to the string scale cutoff.

Contribution

It introduces a simple formula for conical entropy applicable to higher spin fields and applies it to open and closed superstrings, including twisted conical entropy in Melvin backgrounds.

Findings

Entanglement entropy in closed superstring is UV finite.

Derived a new simple formula for conical entropy of free higher spin fields.

Applied the formula to compute entanglement entropy in various string backgrounds.

Abstract

In this paper, we study the entanglement entropy in string theory in the simplest setup of dividing the nine dimensional space into two halves. This corresponds to the leading quantum correction to the horizon entropy in string theory on the Rindler space. This entropy is also called the conical entropy and includes surface term contributions. We first derive a new simple formula of the conical entropy for any free higher spin fields. Then we apply this formula to computations of conical entropy in open and closed superstring. In our analysis of closed string, we study the twisted conical entropy defined by making use of string theory on Melvin backgrounds. This quantity is easier to calculate owing to the folding trick. Our analysis shows that the entanglement entropy in closed superstring is UV finite owing to the string scale cutoff.