Double-trace deformations, mixed boundary conditions and functional determinants in AdS/CFT

According to the AdS/CFT dictionary, perturbing the large N boundary theory by a relevant double-trace deformation of the form f ² corresponds in the bulk to imposing ''mixed'' boundary conditions for the field dual to . In this note we address various aspects of this correspondence. The change c _UV-c _IR of the central charge between the UV and IR fixed points is known from explicit calculations (hep-th/0210093, hep-th/0212138) to be exactly the same in the bulk and in the boundary theories. By comparing the appropriate bulk and boundary functional determinants, we give a simple ''kinematic'' explanation for this universal agreement. We also clarify the prescription for computing AdS/CFT correlators with Δ _- boundary conditions.