Renormalization group flow of entanglement entropy on spheres

TL;DR

This paper investigates how entanglement entropy evolves under renormalization group flow on spheres in de Sitter space, revealing relations with the energy-momentum tensor and universal behaviors at fixed points.

Contribution

It establishes a relation between entanglement entropy RG flow and the energy-momentum tensor trace, and explores universal contributions and fixed point behaviors in various dimensions.

Findings

Entanglement entropy in de Sitter space equals static patch thermal entropy.

Universal contributions match known results for free fields and fixed points.

In three dimensions, the renormalized entanglement entropy is stationary but not monotonic.

Abstract

We explore entanglement entropy of a cap-like region for a generic quantum field theory residing in the Bunch-Davies vacuum on de Sitter space. Entanglement entropy in our setup is identical with the thermal entropy in the static patch of de Sitter, and we derive a simple relation between the vacuum expectation value of the energy-momentum tensor trace and the RG flow of entanglement entropy. In particular, renormalization of the cosmological constant and logarithmic divergence of the entanglement entropy are interrelated in our setup. We confirm our findings by recovering known universal contributions for a free field theory deformed by a mass operator as well as obtain correct universal behaviour at the fixed points. Simple examples of entanglement entropy flows are elaborated in $d=2,3,4$. In three dimensions we find that while the renormalized entanglement entropy is stationary at the fixed points, it is not monotonic. We provide a computational evidence that the universal `area law' for a conformally coupled scalar is different from the known result in the literature, and argue that this difference survives in the limit of flat space. Finally, we carry out the spectral decomposition of entanglement entropy flow and discuss its application to the F-theorem.