Complementarity of the Maldacena and Karch-Randall pictures

We perform a one-loop test of the holographic interpretation of the Karch-Randall model, whereby a massive graviton appears on an ${\mathrm{AdS}}_{4}$ brane in an ${\mathrm{AdS}}_{5}$ bulk. Within the AdS/CFT framework, we examine the quantum corrections to the graviton propagator on the brane, and demonstrate that they induce a graviton mass in exact agreement with the Karch-Randall result. Interestingly enough, at one loop order, the spin-0, spin-1/2, and spin-1 loops contribute to the dynamically generated $(\mathrm{mass}{)}^{2}$ in the same $1:3:12$ ratio as enter the Weyl anomaly and the ${1/r}^{3}$ corrections to the Newtonian gravitational potential.