Entanglement entropy of singular surfaces under relevant deformations in holography
arXiv:1709.08169 · doi:10.1007/JHEP02(2018)009
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.
21 pages. v2: 30 pages, title changed, one section regarding the renormalization added, minor corrections in text and equations
References in corpus (15)
- Towards a derivation of holographic entanglement entropy
- Area laws in quantum systems: mutual information and correlations
- Holographic c-theorems in arbitrary dimensions
- Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
- Entanglement entropy, conformal invariance and extrinsic geometry
- On Holographic Entanglement Entropy and Higher Curvature Gravity
- Universal terms for the entanglement entropy in 2+1 dimensions
- Universality of corner entanglement in conformal field theories
- Some Calculable Contributions to Entanglement Entropy
- On Shape Dependence and RG Flow of Entanglement Entropy
- Entanglement Entropy for Relevant and Geometric Perturbations
- Entanglement entropy for a Dirac fermion in three dimensions: vertex contribution
- Renormalized entanglement entropy
- Relevant Perturbation of Entanglement Entropy and Stationarity
- Holographic torus entanglement and its RG flow