Obstructions to the Existence of Sasaki-Einstein Metrics

Details Obstructions to the Existence of Sasaki-Einstein Metrics Obstructions to the Existence of Sasaki-Einstein Metrics

2006-07-12

arxiv.org/abs/hep-th/0607080v2

Commun.Math.Phys.273:803-827,2007

Physics

High Energy Physics

High Energy Physics - Theory

35 pages, 1 figure; references and a footnote added

Scientific paper

10.1007/s00220-007-0213-7

We describe two simple obstructions to the existence of Ricci-flat Kahler cone metrics on isolated Gorenstein singularities or, equivalently, to the existence of Sasaki-Einstein metrics on the links of these singularities. In particular, this also leads to new obstructions for Kahler-Einstein metrics on Fano orbifolds. We present several families of hypersurface singularities that are obstructed, including 3-fold and 4-fold singularities of ADE type that have been studied previously in the physics literature. We show that the AdS/CFT dual of one obstruction is that the R-charge of a gauge invariant chiral primary operator violates the unitarity bound.

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