  We compute entanglement entropy for free massive scalar fields in anti-de
Sitter (AdS) space. The entangling surface is a minimal surface whose boundary
is a sphere at the boundary of AdS. The entropy can be evaluated from the
thermal free energy of the fields on a topological black hole by using the
replica method. In odd-dimensional AdS, exact expressions of the Renyi entropy
$S_n$ are obtained for arbitrary $n$. We also evaluate 1-loop corrections
coming from the scalar fields to holographic entanglement entropy. Applying the
results, we compute the leading difference of entanglement entropy between two
holographic CFTs related by a renormalization group flow triggered by a double
trace deformation. The difference is proportional to the shift of a central
charge under the flow.
