Entanglement entropy of linearized gravitons in a sphere

TL;DR

This work computes the entanglement entropy of free gravitons in flat space for a spherical region by fixing a gauge compatible with spherical symmetry, showing the EE reduces to that of two scalar-like radial modes after removing the $l=0$ and $l=1$ sectors. The analysis establishes a precise correspondence between the gauge-fixed graviton degrees of freedom inside the sphere and gauge-invariant curvature operators, enabling a direct EE calculation via scalar-field techniques. The main result is a universal logarithmic coefficient of $-rac{61}{45}$ for the sphere, matching the corresponding scalar-based mutual information, and it is shown that the graviton EE on the sphere is equivalent to two scalar fields with the low-angular-momentum modes removed. These findings illuminate localization of gauge-invariant algebras in curved regions and suggest how higher-spin fields would contribute in a similar subtraction scheme.

Abstract

We compute the entanglement entropy of a massless spin $2$ field in a sphere in flat Minkowski space. We describe the theory with a linearized metric perturbation field $h_{μν}$ and decompose it in tensor spherical harmonics. We fix the gauge such that a) the two dynamical modes for each angular momentum decouple and have the dynamics of scalar spherical modes, and b) the gauge-fixed field degrees of freedom inside the sphere represent gauge invariant operators of the theory localized in the same region. In this way the entanglement entropy turns out to be equivalent to the one of a pair of free massless scalars where the contributions of the $l=0$ and $l=1$ modes have been subtracted. The result for the coefficient of the universal logarithmic term is $-61/45$ and coincides with the one computed using the mutual information.

Figures (1)

• Figure 1: Two parallel planes with a separation of distance $L$ in the $x^1$ direction.