The paper claims, via mirror symmetry and a quiver search, that none of a listed set of cE6 and cE7 singularities admit crepant resolutions and hence lack N=1 quiver SCFT duals.
On the Superconformal Index of N=1 IR Fixed Points: A Holographic Check
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We evaluate the superconformal index of the Y^{p,q} quiver gauge theories using Romeslberger's prescription. For the conifold quiver Y^{1,0} we find exact agreement at large N with a previous calculation in the dual AdS_5 X T^{1,1} supergravity.
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On holographic duals of certain isolated weighted Gorenstein cDV singularities
The paper claims, via mirror symmetry and a quiver search, that none of a listed set of cE6 and cE7 singularities admit crepant resolutions and hence lack N=1 quiver SCFT duals.