On Shape Dependence and RG Flow of Entanglement Entropy

TL;DR

This paper investigates how the shape of entangling surfaces affects entanglement entropy in various quantum field theories using both field theoretic and holographic methods, revealing shape-dependent divergences and monotonic RG flow behavior.

Contribution

It provides new insights into shape dependence of entanglement entropy in conformal and gapped theories, including explicit calculations and a holographic dual construction.

Findings

Shape-dependent divergent terms in 3+1D conformal field theories.

Expansion of entanglement entropy in inverse odd powers of mass in 2+1D theories.

Renormalized entanglement entropy is monotonic along RG flow.

Abstract

We use a mix of field theoretic and holographic techniques to elucidate various properties of quantum entanglement entropy. In (3+1)-dimensional conformal field theory we study the divergent terms in the entropy when the entangling surface has a conical or a wedge singularity. In (2+1)-dimensional field theory with a mass gap we calculate, for an arbitrary smooth entanglement contour, the expansion of the entropy in inverse odd powers of the mass. We show that the shape-dependent coefficients that arise are even powers of the extrinsic curvature and its derivatives. A useful dual construction of a (2+1)-dimensional theory, which allows us to exhibit these properties, is provided by the CGLP background. This smooth warped throat solution of 11-dimensional supergravity describes renormalization group flow from a conformal field theory in the UV to a gapped one in the IR. For this flow we calculate the recently introduced renormalized entanglement entropy and confirm that it is a monotonic function.