AdS gravity, SO(2,d) gauge theory and Holography.
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 explained as the SO(2,d) conservation law under a local energy scale of the dual CFT. Providing these conservation laws as well as a SO(2,d) covariant area law are valid for any local energy scale, the bulk Einstein equation will be automatically implied.
Publisher URL: http://arxiv.org/abs/1811.05286