2006/07/31 by Jerome P. Gauntlett, Dario Martelli, James Sparks +1
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #hep-th #math.DG
paper · pdf · doi:10.1007/s00220-007-0213-7
published as Commun.Math.Phys.273:803-827,2007 · 35 pages, 1 figure; references and a footnote added
arxiv created 2006/08/17 · openalex publication_date 2007/05/03 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01
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.