Entanglement measures for non-conformal D-branes

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 ${\text{I}}_M$ continuously decreases to zero for the aforementioned configurations. We also notice that the conjectured inequality ${\text{E}}_W\ge {\text{I}}_M/2$ 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.

arXiv comment21 pages, 6 figures; the analysis has been substantially modified; references added; accepted for publication in Physical Review D

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