Complementarity of the Maldacena and Randall-Sundrum Pictures

We revive an old result, that one-loop corrections to the graviton propagator induce $1/r^3$ corrections to the Newtonian gravitational potential, and compute the coefficient due to closed loops of the $\mathrm{U}\left(N\right)$ $N=4\mathrm{}$ super-Yang-Mills theory that arises in Maldacena's anti–de Sitter conformal field theory correspondence. We find exact agreement with the coefficient appearing in the Randall-Sundrum brane-world proposal. This provides more evidence for the complementarity of the two pictures.