# Boundaries of zero scalar curvature in the AdS / CFT correspondence

@article{Cai1999BoundariesOZ, title={Boundaries of zero scalar curvature in the AdS / CFT correspondence}, author={Mingliang Cai and Gregory J. Galloway}, journal={Advances in Theoretical and Mathematical Physics}, year={1999}, volume={3}, pages={1769-1783} }

In hep-th/9910245, Witten and Yau consider the AdS/CFT correspondence in the context of a Riemannian Einstein manifold $M^{n+1}$ of negative Ricci curvature which admits a conformal compactification with conformal boundary $N^n$. They prove that if the conformal class of the boundary contains a metric of positive scalar curvature, then $M$ and $N$ have several desirable properties: (1) $N$ is connected, (2) the $n$th homology of the compactified $M$ vanishes, and (3) the fundamental group of $M…

## 36 Citations

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