Entanglement measures for non-conformal D-branes

TL;DR

This paper investigates entanglement measures in non-conformal D-brane backgrounds, analyzing holographic entanglement entropy and entanglement wedge cross section at various temperatures, revealing monotonic behaviors, phase transitions, and the validity of certain inequalities.

Contribution

It provides explicit calculations of entanglement measures for non-conformal D$p$-brane backgrounds, extending understanding beyond conformal cases and confirming conjectured inequalities.

Findings

$ ext{E}_{W}$ decreases monotonically with temperature

Discontinuous jumps in $ ext{E}_{W}$ at critical subregion separations

Mutual information $ exttt{I}_{M}$ decreases continuously to zero

Abstract

We study various entanglement measures associated with certain non-conformal field theories. We consider non-conformal D$p$-brane backgrounds, which are dual to these field theories, for our holographic analysis. Restricting our interests in $p=1,2,4$, we explicitly compute properties of holographic entanglement entropy and entanglement wedge cross section, $\text{E}_{W}$, corresponding to two parallel strip shaped boundary subregions in these set ups. We study low and high temperature behaviours of these quantities analytically as well as using numerical methods. In all cases, the $\text{E}_{W}$ decrease monotonically with temperature. We observe discontinuous jumps in $\text{E}_{W}$ while the width of (as well as the separation between) the subregions reach critical values in all the cases considered. However, the corresponding holographic mutual information $\texttt{I}_{M}$ continuously decreases to zero for the aforementioned configurations. We also notice that the conjectured inequality $\text{E}_{W} \geq \texttt{I}_{M}/2$ still holds for non-conformal field theories as well. We analytically determine the critical separation between these subregions that triggers a phase transition in the holographic mutual information.