  We compare the one-loop corrections to the entropy of a black hole, from
quantum fields of spin zero, one-half, and one, to the entropy of entanglement
of the fields. For fields of spin zero and one-half the black hole entropy is
identical to the entropy of entanglement. For spin one the two entropies differ
by a contact interaction with the horizon which appears in the black hole
entropy but not in the entropy of entanglement. The contact interaction can be
expressed as a path integral over particle paths which begin and end on the
horizon; it is the field theory limit of the interaction proposed by Susskind
and Uglum which couples a closed string to an open string stranded on the
horizon.
