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Gravity in d dimensions is formulated as the gauge theory of local SO(2,d-1)gauge group. The Chern-Pontryagin index ${\cal P}_{2n}$ plays a crucial role inboth gravity and gauge theories. ${\cal P}_{2n}(gravity)$ gives thegravitational Lagrangian in 2n dimensions, having the vacuum solution$AdS_{2n}$. The same but global symmetry is shared with the gauge theories and0,1-cochains of the Chern-Simon index ${\cal C}_{2n}(gauge)$ take part of$CFT_{2n-1}$ and $CFT_{2n-2}$, respectively. Gravity in odd dimensions is quiteanalogously formulated to that in even dimensions. This gives new insights onAdS/CFT correspondence.

SO(2,d-1) Gauge Theory of Gravity in d Dimensional Spacetime and $AdS_d/CFT_{d-1}$ Correspondence