We study a family of higher-derivative conformal operators $P_{2k}^{(2)}$
acting on transverse-traceless symmetric 2-tensors on generic Einstein spaces.
They are a natural generalization of the well-known construction for scalars.
We first provide the alternative description in terms of a bulk
Poincar\’e-Einstein metric by making use of the AdS/CFT dictionary and argue
that their holographic dual generically consists of bulk massive gravitons. For
special values of the mass, the bulk fields acquire an additional gauge
invariance with vector and scalar gauge parameters in the cases of massless and
partially massless gravitons, respectively. Having clarified the correspondence
at tree level, we move on to the one-loop quantum level and put forward a
holographic formula for the functional determinant of the higher-derivative
conformal operators $P_{2k}^{(2)}$ in terms of the functional determinant for
massive gravitons with standard and alternate boundary conditions. In the
process, the analogous construction for vectors $P_{2k}^{(1)}$ is worked out as
well, and we end up with an interesting recursive structure. Although the
factorization into shifted Lichnerowicz Laplacian is better suited for heat
kernel computations, we are also able to rewrite the holographic formula for
unconstrained vector and traceless symmetric 2-tensor due to the decoupling of
the longitudinal part. The holographic formula also provides the necessary
building blocks to address the special cases of massless and partially massless
bulk gravitons where gauge invariance turns up. In four and six dimensions we
are able to provide evidence for the correctness of the holographic formula by
computing the partition functions and the Weyl anomaly coefficients, verifying
for the latter full agreement between bulk and boundary computations and with
results available in the literature.
