Some Calculable Contributions to Holographic Entanglement Entropy

TL;DR

This work analyzes holographic entanglement entropy under relevant boundary deformations within AdS/CFT. It proves that logarithmic EE coefficients are state-independent and fixed by boundary geometry, even with backreaction from a bulk scalar, and shows that relevant deformations induce new universal logarithmic contributions that couple the deformation scale to intrinsic and extrinsic curvatures of the entangling surface. The authors provide explicit flat- and curved-background calculations for various operator dimensions, exhibiting how the deformation reshapes the universal terms and connects to trace anomalies. They extend PBH methods to matter-coupled bulks, deriving explicit expressions for the state-independent data and the leading universal EE term, and discuss broader implications, including higher-curvature bulk theories and finite-temperature effects on the finite part of EE.

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].