Holographic entanglement entropy of surface defects

TL;DR

This paper computes the holographic entanglement entropy for surface defects in ${ m AdS}_5 imes S^5$ using supergravity solutions, providing new insights into defect contributions and their relation to stress tensor one-point functions.

Contribution

It introduces a novel calculation of entanglement entropy for surface defects in ${ m N}=4$ SYM via holography, combining supergravity solutions with the Lewkowycz-Maldacena method.

Findings

Two consistent expressions for entanglement entropy are obtained.

The defect operator expectation value is explicitly computed.

An additional term in the entropy difference is identified and discussed.

Abstract

We calculate the holographic entanglement entropy in type IIB supergravity solutions that are dual to half-BPS disorder-type surface defects in ${\cal N}=4$ Super Yang-Mills theory. The entanglement entropy is calculated for a ball-shaped region bisected by a surface defect. Using the bubbling supergravity solutions we also compute the expectation value of the defect operator. Combining our result with the previously-calculated one-point function of the stress tensor in the presence of the defect, we adapt the calculation of Lewkowycz and Maldacena to obtain a second expression for the entanglement entropy. Our two expressions agree up to an additional term, whose possible origin and significance is discussed