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 in both gravity and gauge theories. ${ \cal P}_{ 2n}(gravity)$ gives the gravitational Lagrangian in 2n dimensions, having the vacuum solution $AdS_{ 2n}$. The same but global symmetry is shared with the gauge theories and 0,1-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 quite analogously formulated to that in even dimensions. This gives new insights on AdS/CFT correspondence.
Categories: hep-th