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<p>We systematically study the AdS/CFT correspondence induced by D3 branes probing three dimensional Gorenstein quotient singularity <i>ℂ</i><sup>3</sup>/<i>G</i>. The field theory is given by the McKay quiver, which has a vanishing NSVZ beta function assuming that all the chiral fields have the U(1)<sub><i>R</i></sub> charge <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> </math></EquationSource> <EquationSource Format="TEX">\( \frac{2}{3} \)</EquationSource> </InlineEquation>. Various physical quantities such as quiver Hilbert series, superconformal index, central charges, etc are computed, which match exactly with those computed using the singularity. We also study the relevant deformation of those theories and find the dual geometry, therefore generate many new interesting AdS/CFT pairs. The quiver gauge theory defined using finite subgroups of SO(3) group has some interesting features, for example, its Seiberg duality behavior is quite interesting.</p>

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Three dimensional quotient singularity and 4d \( \mathcal{N} \) = 1 AdS/CFT correspondence

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  • 发表日期：

    2026年4月27日

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  • Yuanyuan Fang,
  • Jing Feng,
  • Dan Xie

摘要

We systematically study the AdS/CFT correspondence induced by D3 branes probing three dimensional Gorenstein quotient singularity ℂ3/G. The field theory is given by the McKay quiver, which has a vanishing NSVZ beta function assuming that all the chiral fields have the U(1)R charge 2 3 \( \frac{2}{3} \) . Various physical quantities such as quiver Hilbert series, superconformal index, central charges, etc are computed, which match exactly with those computed using the singularity. We also study the relevant deformation of those theories and find the dual geometry, therefore generate many new interesting AdS/CFT pairs. The quiver gauge theory defined using finite subgroups of SO(3) group has some interesting features, for example, its Seiberg duality behavior is quite interesting.