  We consider the one-loop partition function of free quantum field theory in
locally Anti-de Sitter space-times. In three dimensions, the one loop
determinants for scalar, gauge and graviton excitations are computed explicitly
using heat kernel techniques. We obtain precisely the result anticipated by
Brown and Henneaux: the partition function includes a sum over "boundary
excitations" of AdS3, which are the Virasoro descendants of empty Anti-de
Sitter space. This result also allows us to compute the one-loop corrections to
the Euclidean action of the BTZ black hole as well its higher genus
generalizations.
