Area terms in entanglement entropy

TL;DR

This work demonstrates that universal area terms in entanglement entropy can be robustly defined in flat-space QFT by mutual information regularization, and that Rosenhaus-Smolkin's first-law approach is equivalent to the Adler-Zee expression for renormalization of the Newton constant when evaluated with the correct stress-tensor and modular-Hamiltonian structure. It clarifies how ambiguities from stress-tensor improvement, boundary terms, and contact terms affect the calculations, and provides explicit results for free fields (scalars and fermions) as well as insights for interacting theories via the $O(N)$ model and holographic comparisons. The paper connects area-term running to c-theorems in two and three dimensions, illustrating how universal terms constrain RG flows and the F-theorem, and discusses how these universal quantities inform holographic entropy computations and gravity's role in entanglement. Overall, it establishes a coherent, regulator-independent picture of area terms in EE, highlighting the interplay between quantum field theory in flat space and gravitational renormalization, with implications for holography and quantum information approaches to many-body physics.

Abstract

We discuss area terms in entanglement entropy and show that a recent formula by Rosenhaus and Smolkin is equivalent to the term involving a correlator of traces of the stress tensor in Adler-Zee formula for the renormalization of the Newton constant. We elaborate on how to fix the ambiguities in these formulas: Improving terms for the stress tensor of free fields, boundary terms in the modular Hamiltonian, and contact terms in the Euclidean correlation functions. We make computations for free fields and show how to apply these calculations to understand some results for interacting theories which have been studied in the literature. We also discuss an application to the F-theorem.