Notes on Entanglement Entropy in String Theory

TL;DR

The authors address entanglement entropy in string theory using the replica method, deriving a general conical entropy framework for free higher-spin fields and applying it to open and closed string sectors. They reveal that open-string one-loop conical entropy is UV-divergent without backreaction, whereas closed-string (especially twisted) conical entropy is UV-finite and appears to vanish at one loop, consistent with supersymmetry. The introduction of the Melvin-background twist provides a tractable route to analyze UV/IR behavior and to separate orbifold and twisted-sector contributions, offering insights into how string-scale effects regularize EE and potentially constrain quantum corrections to black hole entropy. The work connects entanglement, holography, and string-theoretic UV completions, suggesting that in highly supersymmetric backgrounds, quantum corrections to horizon entropy may be absent at one loop. A direct, non-perturbative closed-string EE computation remains a key future direction.

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.