On holographic duals of certain isolated weighted Gorenstein cDV singularities

TL;DR

This paper uses homological mirror symmetry to show that certain Gorenstein cDV singularities lack crepant resolutions, preventing their use as holographic backgrounds for specific superconformal gauge theories.

Contribution

It introduces a novel approach based on homological mirror symmetry to prove the non-existence of crepant resolutions for certain singularities.

Findings

Certain singularities cannot serve as holographic backgrounds.

Enumeration confirms no compatible quiver gauge theories exist.

Provides a new mathematical framework for understanding singularities in holography.

Abstract

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.