AdS plane waves, entanglement, and mutual information

Abstract

AdS plane wave backgrounds are dual to CFT excited states with energy momentum density T ++ = Q. Building on previous work on entanglement entropy in these and nonconformal brane plane wave backgrounds, we first describe a phenomenological scaling picture for entanglement in terms of "entangling partons". We then study aspects of holographic mutual information in these backgrounds for two strip shaped subsystems, aligned parallel or orthogonal to the flux. We focus on the wide (Ql d ≫ 1) and narrow (Ql d ≪ 1) strip regimes. In the wide strip regime, mutual information exhibits growth with the individual strip sizes and a disentangling transition as the separation between the strips increases, whose behaviour is distinct from the ground and thermal states. In the narrow strip case, our calculations have parallels with "entanglement thermodynamics" for these AdS plane wave deformations. We also discuss some numerical analysis.

Classification of certain asymptotically AdS space-times with Ricci-flat boundary

“…Some work in this direction has already been pursued, for example the behavior of the entanglement entropy and the mutual information for strip shaped regions has been studied in the case of AdS II + , showing interesting features [2].…”

“…In this sense, the expression (3.19) can be seen as a generalization of the null deformations of AdS studied e.g. in [2,3]. They are not a continuous deformations ofγ µν , and they should not be seen as perturbations of the latter.…”

“…This classification is naturally extended to the corresponding gravity solutions. Next, it is shown that requiring the absence of scalar curvature singularities leads to metrics that can be interpreted as "null deformations" of AdS or of the AdS soliton [2,3].…”

“…In appendix C we show that the solution (2.9) has a scalar curvature singularity unless all but one eigenvalues of the boundary stress tensor T µν are equal to 4e −du 0 . 2 The remaining eigenvalue is determined by (2.11), so we have: 3…”

“…This metric is the prototype of AdS plane wave, which has been studied in particular when γ > 1 [2,3]. We shall denote the above metric by AdS II + when γ = 1, and by AdS II − when γ = −1.…”