Communications in Mathematical Physics

, Volume 273, Issue 3, pp 803–827

Obstructions to the Existence of Sasaki–Einstein Metrics

  • Jerome P. Gauntlett
  • Dario Martelli
  • James Sparks
  • Shing-Tung Yau
Article

DOI: 10.1007/s00220-007-0213-7

Cite this article as:
Gauntlett, J.P., Martelli, D., Sparks, J. et al. Commun. Math. Phys. (2007) 273: 803. doi:10.1007/s00220-007-0213-7

Abstract

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.

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Jerome P. Gauntlett
    • 1
    • 2
  • Dario Martelli
    • 3
  • James Sparks
    • 4
    • 5
  • Shing-Tung Yau
    • 4
  1. 1.Blackett LaboratoryImperial CollegeLondonU.K.
  2. 2.The Institute for Mathematical SciencesImperial CollegeLondonU.K.
  3. 3.Department of PhysicsCERN Theory UnitGeneva 23Switzerland
  4. 4.Department of MathematicsHarvard UniversityCambridgeU.S.A.
  5. 5.Jefferson Physical LaboratoryHarvard UniversityCambridgeU.S.A.