Logarithmic Corrections to the Entanglement Entropy

Abstract

In a $d$-dimensional conformal field theory, it has been known that a relevant deformation operator with the conformal dimension, $\Delta =\frac{d+2}{2}$, generates a logarithmic correction to the entanglement entropy. In the large 't Hooft coupling limit, we can investigate such a logarithmic correction holographically by deforming an AdS space with a massive scalar field dual to the operator with $\Delta =\frac{d+2}{2}$. There are two sources generating the logarithmic correction. One is the metric deformation and the other is the minimal surface deformation. In this work, we investigate the change of the entanglement entropy caused by the minimal surface deformation and find that the second order minimal surface deformation leads to an additional logarithmic correction.

21 pages, reference added

References in corpus (23)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Towards a derivation of holographic entanglement entropy
• Linear Confinement and AdS/QCD
• Holographic c-theorems in arbitrary dimensions
• Giant Magnons
• Entanglement entropy, conformal invariance and extrinsic geometry
• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
• On three-point correlation functions in the gauge/gravity duality
• Some Calculable Contributions to Entanglement Entropy
• Bulk Emergence and the RG Flow of Entanglement Entropy
• Entanglement of Local Operators in large N CFTs
• Entanglement Entropy: A Perturbative Calculation
• On Shape Dependence and RG Flow of Entanglement Entropy
• Entanglement Entropy for Relevant and Geometric Perturbations
• Entanglement entropy, planar surfaces, and spectral functions
• Relevant Perturbation of Entanglement Entropy and Stationarity
• Correlation functions of magnon and spike
• Holographic Entanglement Entropy in 2D Holographic Superconductor via $Ad{S}_3/CF{T}_2$
• Holographic entanglement entropy in the nonconformal medium
• Correlation function of dyonic strings
• Renormalized Entanglement Entropy Flow in Mass-deformed ABJM Theory
• Holographic 1/Nc correction from the chiral condensate
• Holographic Nucleons in the Nuclear Medium

Cited by in corpus (13)

• c-theorem of the entanglement entropy
• RG flow of entanglement entropy to thermal entropy
• Thermodynamic law from the entanglement entropy bound
• On the Shape Dependence of Entanglement Entropy
• Entanglement and RG in the $O(N)$ vector model
• Holographic Approach to Entanglement Entropy in Disordered Systems
• Holographic Entanglement Entropy of Anisotropic Minimal Surfaces in LLM Geometries
• Entanglement entropy of singular surfaces under relevant deformations in holography
• Quantum correlation in quark-gluon medium
• Holographic entanglement entropy probe on spontaneous symmetry breaking with vector order
• Curved Corner Contribution to the Entanglement Entropy in an Anisotropic Spacetime
• Entanglement entropy and complexity of singular subregions in deformed CFT
• Relevant perturbation of entanglement entropy of singular surfaces