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A<sc>bstract</sc> We explore a new approach to boundaries and interfaces in theO(N) model where we add certain localized cubic interactions. These operators are nearly marginal when the bulk dimension is 4 −ϵ, and they explicitly break theO(N) symmetry of the bulk theory down toO(N− 1). We show that the one-loop beta functions of the cubic couplings are affected by the quartic bulk interactions. For the interfaces, we find real fixed points up to the critical valueN_crit≈ 7, while forN >4 there are IR stable fixed points with purely imaginary values of the cubic couplings. For the boundaries, there are real fixed points for allN, but we don’t find any purely imaginary fixed points. We also consider the theories ofMpairs of symplectic fermions and one real scalar, which have quartic OSp(1|2M) invariant interactions in the bulk. We then add the Sp(2M) invariant localized cubic interactions. The beta functions for these theories are related to those in theO(N) model via the replacement ofNby 1 − 2M. In the special caseM= 1, there are boundary or interface fixed points that preserve the OSp(1|2) symmetry, as well as other fixed points that break it.