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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal{N}=1\)</EquationSource> </InlineEquation> 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.</p>

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On holographic duals of certain isolated weighted homogeneous Gorenstein cDV singularities

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月26日

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  • Yuanyuan Fang,
  • Zekai Yu

摘要

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 \(\mathcal{N}=1\) 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.