Logarithmic Corrections to the Entanglement Entropy

TL;DR

This paper explores how minimal surface deformations in holographic models of conformal field theories lead to additional logarithmic corrections to entanglement entropy, extending previous understanding of such corrections.

Contribution

It demonstrates that second order minimal surface deformations contribute extra logarithmic corrections to entanglement entropy in holographic models.

Findings

Second order minimal surface deformation causes additional logarithmic correction.

Logarithmic corrections originate from both metric and surface deformations.

Holographic analysis confirms the role of minimal surface deformation in entanglement entropy corrections.

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.