  In this paper we consider entanglement entropies in two-dimensional conformal
field theories in the presence of topological interfaces. Tracing over one side
of the interface, the leading term of the entropy remains unchanged. The
interface however adds a subleading contribution, which can be interpreted as a
relative (Kullback-Leibler) entropy with respect to the situation with no
defect inserted. Reinterpreting boundaries as topological interfaces of a
chiral half of the full theory, we rederive the left/right entanglement entropy
in analogy with the interface case. We discuss WZW models and toroidal bosonic
theories as examples.
