In 2006, Ryu and Takayanagi provided a general recipe on how to compute
entanglement entropy of a Conformal Field Theory using gauge/gravity
duality. This holographic prescription, which considers the extension of
the entangling region from the boundary into an Einstein space bulk, has
produced remarkable insight on general properties of strongly correlated
systems. However, this progress has been made on a rather case-by-case
basis, as it requires proper renormalization of the gravity action in
the bulk.

In this talk, we introduce a more geometric approach to deal with the
above problem. By the addition of topological terms to the gravity
action, we renormalize the holographic entanglement entropy and relate
holographic properties of CFTs to a topological number (Euler
characteristic).