  We show that the relation between the 't Hooft coupling and the radius of AdS
is not renormalized at one-loop in the sigma model perturbation theory. We
prove this by computing the quantum effective action for the superstring on
AdS_5 x S^5 and showing that it does not receive any finite alpha' corrections.
We also show that the central charge of the interacting worldsheet conformal
field theory vanishes at one-loop.
