A bstract 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.
Fang et al. (2026) studied this question.