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

TL;DR

This paper formulates gravity as an SO(2,d-1) gauge theory in d dimensions, revealing new insights into the AdS/CFT correspondence through the role of Chern-Pontryagin and Chern-Simons indices.

Contribution

It introduces a gauge-theoretic formulation of gravity in arbitrary dimensions using SO(2,d-1) symmetry, linking gravitational and gauge topological invariants to AdS/CFT correspondence.

Findings

Gravity in even dimensions derived from Chern-Pontryagin index.

Gravity in odd dimensions formulated similarly to even dimensions.

New insights into AdS/CFT correspondence from gauge theory perspective.

Abstract

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.