We construct unitary, stable, and interacting conformal boundary conditions for a free massless scalar in four dimensions by coupling it to edge modes living on a boundary. The boundary theories we consider are bosonic and fermionic QED 3 with N f flavors and a Chern-Simons term at level k, in the large-N f limit with fixed k/N f . We find that interacting boundary conditions only exist when k ̸ = 0. To obtain this result we compute the β functions of the classically marginal couplings at the first non-vanishing order in the large-N f expansion, and to all orders in k/N f and in the couplings. To check vacuum stability we also compute the large-N f effective potential. We compare our results with the the known conformal bootstrap bounds.