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

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

2009-02-17

arxiv.org/abs/0902.2820v2

Physics

High Energy Physics

High Energy Physics - Theory

11pages, no figure Typos are corrected. Some comments and references are added

Scientific paper

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.

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