  We argue that multi-trace interactions in quantum field theory on the
boundary of AdS space can be incorporated in the AdS/CFT correspondence by
using a more general boundary condition for the bulk fields than has been
considered hitherto. We illustrate the procedure for a renormalizable
four-dimensional field theory with a $(\Tr \Phi^2)^2$ interaction. In this
example, we show how the AdS fields with the appropriate boundary condition
reproduce the renormalization group effects found in the boundary field theory.
We also construct in related examples a line of fixed points with a
nonperturbative duality, and a flow between two methods of quantization.
