Gravitons on the edge

TL;DR

This paper investigates graviton entanglement in Minkowski space using Euclidean path integrals, revealing the role of edge modes related to large diffeomorphisms at the Rindler horizon and connecting to electromagnetic edge modes.

Contribution

It introduces a novel analysis of graviton edge modes via conical entropy, extending Kabat's method and linking large diffeomorphisms to horizon degrees of freedom.

Findings

Conical entropy includes a contact term from horizon vector fields.

Graviton edge modes correspond to large diffeomorphisms at the horizon.

Results suggest a connection between graviton and electromagnetic edge modes.

Abstract

We study free graviton entanglement between Rindler wedges in the Minkowski vacuum state via the Euclidean path integral. We follow Kabat's method for computing the conical entropy, using the heat kernel on the cone with the tip removed, whose resulting von Neumann entropy for photons correctly predicted electromagnetic edge modes. We find that, in addition to the bulk graviton contributions, the conical entropy has a contact term that can be attributed to a vector field anchored to the (d-2)-dimensional (Euclidean) Rindler horizon whose contribution equals d-2 times Kabat's contact term for photons. We suggest that graviton edge modes are hence the d-2 large diffeomorphisms which act internally within the Rindler horizon. Along the way, we address several known issues regarding graviton entanglement. We furthermore sketch how our results may be used to study edge modes in closed bosonic string theory.