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.
Highlights
The gauge/gravity duality [1,2,3] has enriched our understanding of concepts related to quantum information theory
Perhaps the most prominent of all these examples is the holographic computations of entanglement entropy of the dual boundary theory of interest, which is useful in determining the entanglement entropy of pure states [4,5,6,7,8]. This holographic entanglement entropy (HEE) proposal presents an interpretation of the entanglement entropy of the boundary field theory in terms of a geometric quantity, namely, the minimal surface, which is extended into the bulk
A related quantity known as the holographic mutual information (HMI), IMðA; BÞ, between two disjoint boundary intervals A and B can be determined [9,10,11,12]
Summary
The gauge/gravity duality [1,2,3] has enriched our understanding of concepts related to quantum information theory. Very recently, based on the formalism developed in [13,14], various properties of EWCS, along with HEE and HMI, have been studied in different holographic setups [19,20,21,22,23,24].3 All these examples mostly deal with conformal boundary theories, in which cases, the. The purpose of the present paper is to extend the study of certain aspects of EWCS, HEE, and HMI to nonconformal field theories, which are dual to nonconformal Dp-branes [28,29,30,31,32].
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