Connectedness of the boundary in the AdS/CFT correspondence

Edward Witten, S. T. Yau

Research output: Contribution to journalArticlepeer-review

110 Scopus citations


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 N of positive scalar curvature. We show that under these conditions, Hn(M;Z) = 0 and in particular N must be connected. These results resolve some puzzles concerning the AdS/CFT correspondence.

Original languageEnglish (US)
Pages (from-to)1-19
Number of pages19
JournalAdvances in Theoretical and Mathematical Physics
Issue number6
StatePublished - Nov 1999
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • General Physics and Astronomy


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