Connectedness Of The Boundary In The AdS/CFT Correspondence
Edward Witten, S. -T. Yau
Abstract
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.
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