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

Fusion of conformal defects in interacting theories