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

Takeshi Fukuyama

paper

SO(2,d-1) Gauge Theory of Gravity in d Dimensional Spacetime and $A d S_{d} / C F T_{d - 1}$ Correspondence

arXiv:0902.2820

Abstract

Gravity in d dimensions is formulated as the gauge theory of local SO(2,d-1) gauge group. The Chern-Pontryagin index $P_{2 n}$ plays a crucial role in both gravity and gauge theories. $P_{2 n} (g r a v i t y)$ gives the gravitational Lagrangian in 2n dimensions, having the vacuum solution $A d S_{2 n}$ . The same but global symmetry is shared with the gauge theories and 0,1-cochains of the Chern-Simon index $C_{2 n} (g a ug e)$ take part of $C F T_{2 n - 1}$ and $C F T_{2 n - 2}$ , respectively. Gravity in odd dimensions is quite analogously formulated to that in even dimensions. This gives new insights on AdS/CFT correspondence.

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

SO(2,d-1) Gauge Theory of Gravity in d Dimensional Spacetime and AdSd​/CFTd−1​ Correspondence

Abstract

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SO(2,d-1) Gauge Theory of Gravity in d Dimensional Spacetime and $A d S_{d} / C F T_{d - 1}$ Correspondence