  We study a number of (3+1)- and (2+1)-dimensional defect and boundary
conformal field theories holographically dual to supergravity theories. In all
cases the defects or boundaries are planar, and the defects are
codimension-one. Using holography, we compute the entanglement entropy of a
(hemi-)spherical region centered on the defect (boundary). We define defect and
boundary entropies from the entanglement entropy by an appropriate background
subtraction. For some (3+1)-dimensional theories we find evidence that the
defect/boundary entropy changes monotonically under certain renormalization
group flows triggered by operators localized at the defect or boundary. This
provides evidence that the g-theorem of (1+1)-dimensional field theories
generalizes to higher dimensions.
