  In the context of boundary conformal field theory, we derive a sum rule that
relates two and three point functions of the displacement operator. For four
dimensional conformal field theory with a three dimensional boundary, this sum
rule in turn relates the two boundary contributions to the anomaly in the trace
of the stress tensor. We check our sum rule for a variety of free theories and
also for a weakly interacting theory, where a free scalar in the bulk couples
marginally to a generalized free field on the boundary.
