On the Renormalization of Entanglement Entropy

TL;DR

This paper demonstrates that entanglement entropy in a scalar quantum field theory can be renormalized at first order in the coupling constant, supporting its status as a physical, well-defined quantity.

Contribution

It shows that entanglement entropy in a 3+1D scalar field theory is renormalizable at order λ when all relevant operators are included, linking it to black hole entropy interpretations.

Findings

Entanglement entropy is renormalizable at order λ.

The theory remains well-defined with all relevant operators included.

Supports the physical relevance of entanglement entropy.

Abstract

The renormalization of entanglement entropy of quantum field theories is investigated in the simplest setting with a $\lambda \phi^4$ scalar field theory. The 3+1 dimensional spacetime is separated into two regions by an infinitely flat 2-dimensional interface. The entanglement entropy of the system across the interface has an elegant geometrical interpretation using the replica trick, which requires putting the field theory on a curved spacetime background. We demonstrate that the theory, and hence the entanglement entropy, is renormalizable at order $\lambda$ once all the relevant operators up to dimension-4 are included in the action. This exercise has a one-to-one correspondence to entanglement entropy interpretation of the black hole entropy which suggests that our treatment is sensible. Our study suggests that entanglement entropy is renormalizable and is a physical quantity.