Entanglement entropy of singular surfaces under relevant deformations in holography

TL;DR

This paper investigates how relevant perturbations affect the entanglement entropy of singular surfaces in holography, revealing new universal logarithmic terms and divergences influenced by the perturbation and gravity corrections.

Contribution

It introduces the effects of relevant deformations on entanglement entropy for singular surfaces in holography, including new logarithmic terms and divergences, extending previous conformal results.

Findings

Discovery of a new logarithmic term due to relevant perturbation.

Identification of a power law divergence in holographic entanglement entropy.

Introduction of a renormalized entanglement entropy for kink regions.

Abstract

In the vacuum state of a CFT, the entanglement entropy of singular surfaces contains a logarithmic universal term which is only due to the singularity of the entangling surface. We consider the relevant perturbation of a three dimensional CFT for singular entangling surface. We observe that in addition to the universal term due to the entangling surface, there is a new logarithmic term which corresponds to a relevant perturbation of the conformal field theory with a coefficient depending on the scaling dimension of the relevant operator. We also find a new power law divergence in the holographic entanglement entropy. In addition, we study the effect of a relevant perturbation in the Gauss-Bonnet gravity for a singular entangling surface. Again a logarithmic term shows up. This new term is proportional to both the dimension of the relevant operator and the Gauss-Bonnet coupling. We also introduce the renormalized entanglement entropy for a kink region which in the UV limit reduces to a universal positive finite term.