Conformal Symmetry of Supergravities in AdS spaces

Abstract

We show that the background field method applied to supergravity in adS space-time provides the path integral for the theory in the bulk with conformal symmetry associated with the isometry of the adS space. This in turn allows to establish the rigid conformal invariance of the generating functional for the supergravity correlators on the boundary.

14 pages, Latex

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• Resolution a la Kronheimer of ${\mathbb{C}}^3/\Gamma$ singularities and the Monge-Ampere equation for Ricci-flat Kaehler metrics in view of D3-brane solutions of supergravity
• The role of PSL(2,7) in M-theory: M2-branes, Englert equation and the septuples
• Crepant Resolutions of ${\mathbb{C}}^3/{\mathbb{Z}}_4$ and the Generalized Kronheimer Construction (in view of the Gauge/Gravity Correspondence)
• The Integral Form of D=3 Chern-Simons Theories Probing ${\mathbb{C}}^n/\Gamma$ Singularities
• The ${\mathcal{N}}_3=3\to {\mathcal{N}}_3=4$ enhancement of Super Chern-Simons theories in $D=3$, Calabi HyperKähler metrics and M2-branes on the $\mathcal{C}({\mathrm{N}}^{0,1,0})$ conifold
• D3-brane supergravity solutions from Ricci-flat metrics on canonical bundles of Kähler-Einstein surfaces