Entanglement Entropy of a Scalar Field in Anti-de Sitter Space

TL;DR

This paper investigates the entanglement entropy of a free scalar field in (3+1)-dimensional Anti-de Sitter space, analyzing UV divergences, coefficients, and their relation to conformal anomalies.

Contribution

It provides a detailed analysis of entanglement entropy in AdS space, including numerical coefficients and the link to conformal anomalies, which was not previously detailed.

Findings

Identified the structure of UV-divergent terms in the entanglement entropy.

Computed numerical coefficients for these divergences.

Confirmed the relation between the logarithmic term coefficient and conformal anomaly.

Abstract

We study the entanglement entropy of a free massive scalar field at its ground state in (3+1)-dimensional AdS space in global coordinates. We consider spherical entangling surfaces centered at the origin of AdS. We determine the structure of the UV-divergent terms in the entanglement entropy and compute the numerical values of the respective coefficients. We confirm the connection between the coefficient of the logarithmic term and the conformal anomaly.