  We suggest that the principle of holographic duality can be extended beyond
conformal invariance and AdS isometry. Such an extension is based on a special
relation between functional determinants of the operators acting in the bulk
and on its boundary, provided that the boundary operator represents the inverse
propagators of the theory induced on the boundary by the Dirichlet boundary
value problem from the bulk spacetime. This relation holds for operators of
general spin-tensor structure on generic manifolds with boundaries irrespective
of their background geometry and conformal invariance, and it apparently
underlies numerous $O(N^0)$ tests of AdS/CFT correspondence, based on direct
calculation of the bulk and boundary partition functions, Casimir energies and
conformal anomalies. The generalized holographic duality is discussed within
the concept of the "double-trace" deformation of the boundary theory, which is
responsible in the case of large $N$ CFT coupled to the tower of higher spin
gauge fields for the renormalization group flow between infrared and
ultraviolet fixed points. Potential extension of this method beyond one-loop
order is also briefly discussed.
