  The aim of this note is to unveil a striking equivalence between the one-loop
divergences in 7D Einstein and 6D Conformal Gravities. The particular
combination of 6D pointwise Weyl invariants of the 6D Conformal Gravity
corresponds to that of Branson's Q-curvature and can be written solely in terms
of the Ricci tensor and its covariant derivatives. The quadratic metric
fluctuations of this action, 6D Weyl graviton, are endowed with a sixth-order
kinetic operator that happens to factorize on a 6D Einstein background into
product of three shifted Lichnerowicz Laplacians. We exploit this feature to
use standard heat kernel techniques and work out in one go the UV logarithmic
divergences of the theory that contains in this case the four Weyl anomaly
coefficients. In a seemingly unrelated computation, we determine the one-loop
IR logarithmic divergences of 7D Einstein Gravity in a particular 7D
Poincar\'e-Einstein background that is asymptotically hyperbolic and has the
above 6D Einstein manifold at its conformal infinity or boundary. We show the
full equivalence of both computations, as an outgrowth of the IR/UV connection
in AdS/CFT correspondence, and in this way the time-honoured one-loop
calculations in Einstein and higher-derivative gravities take an interesting
new turn.
