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.

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