Obstructions to the existence of Sasaki-Einstein metrics

Journal article

We describe two simple obstructions to the existence of Ricci-flat Kähler 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 Kähler-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. © Springer-Verlag 2007.

Authors: Gauntlett, J; Martelli, D; Sparks, J; Yau, S

• Publication status: Published
• Journal: COMMUNICATIONS IN MATHEMATICAL PHYSICS
• Volume: 273
• Issue: 3
• Pages: 803-827
• Publication date: 2007-08-01
• DOI: 10.1007/s00220-007-0213-7
• EISSN: 1432-0916
• ISSN: 0010-3616
• Language: English