AdS plane waves, entanglement, and mutual information

Anti-de Sitter plane wave backgrounds are dual to conformal field theory 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 ($Q{l}^d\gg 1$) and narrow ($Q{l}^d\ll 1$) 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, for which the behavior is distinct from the ground and thermal states. In the narrow strip case, our calculations have parallels with “entanglement thermodynamics” for these anti-de Sitter plane wave deformations. We also discuss some numerical analyses.

Figure 1

Two parallel disjoint strip subsystems of width $l$ and separation $x$ (and longitudinal size $V_{d-2}$) (left), with the disconnected extremal surface (top right) and the connected extremal surface (bottom right).

Figure 2

Plots of the finite parts of entanglement entropy for the ${\mathrm{AdS}}_4$ ground state (red) and the ${\mathrm{AdS}}_4$ plane wave (the black, green, and blue curves correspond to the values $Q=1$, 3, 10, respectively).

Figure 3

Plots of the finite parts of entanglement entropy for the ${\mathrm{AdS}}_5$ ground state (red) and the ${\mathrm{AdS}}_5$ plane wave (the black, green, and blue curves correspond to the values $Q=1$, 3, 10, respectively).

Figure 4

Plot of the mutual information vs $\frac{x}{l}$ with fixed width $l$ for the ${\mathrm{AdS}}_5$ plane wave.

Figure 5

Plot of the $\frac{x}{l}$ vs $l{Q}^{1/d}$ parameter space with nonzero mutual information for the ${\mathrm{AdS}}_5$ plane wave.