  We consider two conformal defects close to each other in a free theory, and
study what happens as the distance between them goes to zero. This limit is the
same as zooming out, and the two defects have fused to another defect. As we
zoom in we find a non-conformal effective action for the fused defect. Among
other things this means that we cannot in general decompose the two-point
correlator of two defects in terms of other conformal defects. We prove the
fusion using the path integral formalism by treating the defects as sources for
a scalar in the bulk.
