Proof of the Witten-Yau Conjecture

The Witten-Yau theorem in the AdS/CFT correspondence conjectures that the conformal boundary to AdS space must possess a metric of non-negative scalar curvature for the conformal field theory defined thereon to be free of pathologies. By employing various tools from conformal geometry - such as almost Einstein structures, collapsing sphere products and tractor bundles - we rigorously prove this conjecture.