Boundary Conditions and Entanglement in Anti-de Sitter Space

We study the entanglement entropy of a conformally coupled scalar field at its ground state in $(3+1)$-dimensional AdS space in global coordinates. We consider spherical entangling surfaces centered at the origin of AdS and allow for general boundary conditions at the conformal boundary. Through numerical and analytical means, we show that the UV-divergent part of the entropy has a universal form, while the UV-finite part is sensitive to the boundary conditions. We determine the dependence of the latter part on mixed boundary conditions that interpolate between Dirichlet and Neumann.