Quantum Entanglement Index in String Theory

TL;DR

This paper introduces a quantum entanglement index for black hole horizons in string theory, computed via a stringy replica method, revealing finite, tachyon-free entanglement measures that do not require analytic continuation.

Contribution

It defines a new entanglement index in string theory and computes it for BTZ black holes using a novel stringy replica approach, avoiding divergences and tachyons.

Findings

Index is free of tachyons and finite in UV and IR regimes.

Index does not require analytic continuation in N.

Provides a diagnostic tool for entanglement in string theory.

Abstract

We define a notion of `quantum entanglement index' with the aim to compute it for black hole horizons in string theory at one-loop order using the stringy replica method. We consider the horizon of BTZ black holes to construct the relevant conical orbifolds, labeled by an odd integer $N$, and compute the partition function as a function of $N$, corresponding to the fractional indexed R\'enyi entropy. We show that it is free of tachyons and naturally finite both in the ultraviolet and the infrared, even though it is generically ultraviolet divergent in the field theory limit. Thus, the index provides a useful diagnostic of the entanglement structure of string theory without the need for analytic continuation in $N$.