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Connectedness of the boundary in the AdS/CFT correspondence

Edward Witten Shing-Tung Yau

Mathematical Physics mathscidoc:1912.43492

arXiv preprint hep-th/9910245, 1999.10
Let M be a complete Einstein manifold of negative curvature, and assume that (as in the AdS/CFT correspondence) it has a Penrose compactification with a conformal boundary M of positive scalar curvature. We show that under these conditions, M and in particular M must be connected. These results resolve some puzzles concerning the AdS/CFT correspondence.
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@inproceedings{edward1999connectedness,
  title={Connectedness of the boundary in the AdS/CFT correspondence},
  author={Edward Witten, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203601265322056},
  booktitle={arXiv preprint hep-th/9910245},
  year={1999},
}
Edward Witten, and Shing-Tung Yau. Connectedness of the boundary in the AdS/CFT correspondence. 1999. In arXiv preprint hep-th/9910245. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203601265322056.
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