On holographic duals of certain isolated weighted Gorenstein cDV singularities

We employ a novel approach,based on homological mirror symmetry for Landau-Ginzburg models,to demonstrate the non-existence of crepant resolutions for certain weighted homogeneous Gorenstein compound Du Val singularities.Physically,this implies that such singularities cannot serve as holographic backgrounds for four dimensional N=1 superconformal quiver gauge theories realized on the worldvolume of a large number of D3 branes placed at the singular locus.This is confirmed by enumerating all consistent quiver gauge theories.