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Obstructions to the Existence of Sasaki–Einstein Metrics

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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.

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Author information

Authors and Affiliations

  1. Blackett Laboratory, Imperial College, London, SW7 2AZ, U.K.

    Jerome P. Gauntlett

  2. The Institute for Mathematical Sciences, Imperial College, London, SW7 2PG, U.K.

    Jerome P. Gauntlett

  3. Department of Physics, CERN Theory Unit, 1211, Geneva 23, Switzerland

    Dario Martelli

  4. Department of Mathematics, Harvard University, One Oxford Street, Cambridge, MA, 02138, U.S.A.

    James Sparks & Shing-Tung Yau

  5. Jefferson Physical Laboratory, Harvard University, Cambridge, MA, 02138, U.S.A.

    James Sparks

Authors
  1. Jerome P. Gauntlett
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  2. Dario Martelli
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  3. James Sparks
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  4. Shing-Tung Yau
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Correspondence to James Sparks.

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Communicated by G.W. Gibbons

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Gauntlett, J.P., Martelli, D., Sparks, J. et al. Obstructions to the Existence of Sasaki–Einstein Metrics. Commun. Math. Phys. 273, 803–827 (2007). https://doi.org/10.1007/s00220-007-0213-7

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  • DOI: https://doi.org/10.1007/s00220-007-0213-7

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