Some Calculable Contributions to Holographic Entanglement Entropy

TL;DR

This paper investigates how relevant operator deformations affect holographic entanglement entropy, revealing state-independent coefficients for UV-divergent terms and identifying new logarithmic contributions due to the deformation.

Contribution

It establishes that UV-divergent contributions have state-independent coefficients and introduces new logarithmic terms in entanglement entropy caused by relevant deformations.

Findings

UV-divergent coefficients are state-independent

New logarithmic contributions arise from relevant deformations

Similar form of contributions as in free massive scalar field theory

Abstract

Using the AdS/CFT correspondence, we examine entanglement entropy for a boundary theory deformed by a relevant operator and establish two results. The first is that if there is a contribution which is logarithmic in the UV cut-off, then the coefficient of this term is independent of the state of the boundary theory. In fact, the same is true of all of the coefficients of contributions which diverge as some power of the UV cut-off. Secondly, we show that the relevant deformation introduces new logarithmic contributions to the entanglement entropy. The form of some of these new contributions is similar to that found recently in an investigation of entanglement entropy in a free massive scalar field theory [1].