I consider a free Maxwell field in four dimensions in the presence of a codimension two defect. Reflection positive, codimension two defects which preserve conformal symmetry in this context are very limited. Only generalized free fields can exist on the defect and interact with the free Maxwell field in the bulk. This result stands in stark contrast to the codimension one case where interacting conformal boundary conditions can be found for free bulk fields, producing systems with physical relevance, for example for graphene.