  Inspired by the general relation between the boundary global symmetry and the
bulk gauge symmetry in AdS/CFT, we reformulate the $d+1$ dimensional AdS
gravity theory as a $SO(2,d)$ gauge theory. In this formalism, the pull back of
the bulk equation of motion onto a co-dimension one hypersurface $\Sigma$ can
be naturally related to the $SO(2,d)$ conservation law under a local energy
scale in the dual CFT. The consistency of CFT requires that the $SO(2,d)$
covariant anomaly vanishes at arbitrary scale. After imposing a covariant area
law as the renormalization condition, the vanishing of $SO(2,d)$ anomaly
implies that the dual bulk geometries must satisfy the Einstein equation.
