Entanglement entropy of nonlocal theories in AdS spacetimes

We investigate the effect of nonlocality on entanglement entropy in anti–de Sitter spacetime. We compute entanglement entropy of a nonlocal field theory in anti–de Sitter spacetime and find several interesting features. We find that area law is followed, but subleading terms are affected by nonlocality. We also find that the UV-finite term is universal. For the massless theory in three-dimensional anti–de Sitter spacetime we compute it exactly and find the novel feature that it shows oscillatory behavior.

Figure 1

The Green’s function of massless nonlocal scalar field in four spacetime dimensions. The propagator is plotted for various strength of nonlocality $\lambda$ against the spacelike separation $\mu (x,x^{\prime })$.

Figure 2

The Green’s function of the massive nonlocal scalar field in four spacetime dimensions. The propagator is plotted for various masses $m_s$ and for fixed ${\lambda }_s=1$, against the spacelike separation $\mu (x,x^{\prime })$.

Figure 3

Minimal surface corresponding to region $B$ in the boundary. The $z$ direction denotes the bulk while the $x$ represents the spatial coordinate on boundary. The region surrounded by $B$ is $\mathrm{\Sigma }$ and is denoted by $A$.