Holography, Matrix Factorizations and K-stability

Abstract

Placing D3-branes at conical Calabi-Yau threefold singularities produces many AdS${}_5$/CFT${}_4$ duals. Recent progress in differential geometry has produced a technique (called K-stability) to recognize which singularities admit conical Calabi-Yau metrics. On the other hand, the algebraic technique of non-commutative crepant resolutions, involving matrix factorizations, has been developed to associate a quiver to a singularity. In this paper, we put together these ideas to produce new AdS${}_5$/CFT${}_4$ duals, with special emphasis on non-toric singularities.

arXiv comment59 pages, 11 figures, 2 appendices; v2: typos fixed, expanded discussion in section 2.5 and 4.2

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• Coulomb and Higgs Branches from Canonical Singularities: Part 0
• Anomaly Inflow Methods for SCFT Constructions in Type IIB
• Resolution a la Kronheimer of ${\mathbb{C}}^3/\Gamma$ singularities and the Monge-Ampere equation for Ricci-flat Kaehler metrics in view of D3-brane solutions of supergravity
• $\mathcal{N}=1$ conformal dualities from unoriented chiral quivers
• Expanding on the Cardy-like limit of the superconformal index of 4d $\mathcal{N}=1$ ABCD SCFTs
• Futaki Invariants and Reflexive Polygons
• Some Open Questions in Quiver Gauge Theory
• Chiral Rings, Futaki Invariants, Plethystics, and Groebner Bases
• On holographic duals of certain isolated weighted Gorenstein cDV singularities