  We study the effect of a relevant double-trace deformation on the partition
function (and conformal anomaly) of a CFT at large N and its dual picture in
AdS. Three complementary previous results are brought into full agreement with
each other: bulk and boundary computations, as well as their formal identity.
We show the exact equality between the dimensionally regularized partition
functions or, equivalently, fluctuational determinants involved. A series of
results then follows: (i) equality between the renormalized partition functions
for all d; (ii) for all even d, correction to the conformal anomaly; (iii) for
even d, the mapping entails a mixing of UV and IR effects on the same side
(bulk) of the duality, with no precedent in the leading order computations; and
finally, (iv) a subtle relation between overall coefficients, volume
renormalization and IR-UV connection. All in all, we get a clean test of the
AdS/CFT correspondence beyond the classical SUGRA approximation in the bulk and
at subleading O(1) order in the large-N expansion on the boundary.
