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Obstructions to the existence of SasakiEinstein metrics

Jerome P Gauntlett Dario Martelli James Sparks Shing-Tung Yau

Mathematical Physics mathscidoc:1912.43502

Communications in mathematical physics, 273, (3), 803-827, 2007.8
We describe two simple obstructions to the existence of Ricci-flat Khler 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 KhlerEinstein 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 Rcharge of a gauge invariant chiral primary operator violates the unitarity bound.
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@inproceedings{jerome2007obstructions,
  title={Obstructions to the existence of SasakiEinstein metrics},
  author={Jerome P Gauntlett, Dario Martelli, James Sparks, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203635092972066},
  booktitle={Communications in mathematical physics},
  volume={273},
  number={3},
  pages={803-827},
  year={2007},
}
Jerome P Gauntlett, Dario Martelli, James Sparks, and Shing-Tung Yau. Obstructions to the existence of SasakiEinstein metrics. 2007. Vol. 273. In Communications in mathematical physics. pp.803-827. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203635092972066.
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