Fusion of conformal defects in interacting theories

We study fusion of two scalar Wilson defects. We propose that fusion holds at a quantum level by showing that bare one-point functions stay invariant. This is an expected result as the path integral stays invariant under fusion of the two defects. The difference instead lies in renormalization of local quantities on the defects. Those on the fused defect takes into account UV divergences in the fusion limit when the two defects approach eachother, in addition to UV divergences in the coincident limit of defect-local fields and in the near defect limits of bulk-local fields. At the fixed point of the corresponding RG flow the two conformal defects have fused into a single conformal defect.