Entanglement measures for nonconformal D-branes
Arindam Lala
Abstract
We study various entanglement measures associated with certain nonconformal field theories. We consider nonconformal $\mathrm{D}p$-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 the entanglement wedge cross section, ${\mathrm{E}}_{W}$, corresponding to two parallel strip shaped boundary subregions in these setups. We study low and high temperature behaviors of these quantities analytically as well as by using numerical methods. In all cases, the ${\mathrm{E}}_{W}$ decreases monotonically with temperature. We observe discontinuous jumps in ${\mathrm{E}}_{W}$, while the width of (as well as the separation between) the subregions reaches critical values in all the cases considered. However, the corresponding holographic mutual information ${\mathtt{I}}_{M}$ continuously decreases to zero for the aforementioned configurations. We also notice that the conjectured inequality ${\mathrm{E}}_{W}\ensuremath{\ge}{\mathtt{I}}_{M}/2$ still holds for nonconformal field theories as well. We analytically determine the critical separation between these subregions that triggers a phase transition in the holographic mutual information.