Gauge Theory of Gravity and the AdS/CFT Correspondence

We discuss the AdS/CFT correspondence from the viewpoint of gravity as a broken phase of conformal gauge symmetry. In AdS2/CFT1, the Schwarzian structure is related to the boundary extrinsic curvature. In AdS4/CFT3, the gauge-theoretic formulation of four-dimensional gravity contains a boundary-sensitive Euler sector whose descent structure leads to the Cotton tensor characterizing the three-dimensional boundary conformal geometry. At the structural and kinematical level considered here, these results suggest a unified geometrical interpretation of holography in terms of boundary remnants of broken bulk conformal gauge symmetry.