Quivers from Matrix Factorizations

Abstract

We discuss how matrix factorizations offer a practical method of computing the quiver and associated superpotential for a hypersurface singularity. This method also yields explicit geometrical interpretations of D-branes (i.e., quiver representations) on a resolution given in terms of Grassmannians. As an example we analyze some non-toric singularities which are resolved by a single CP1 but have "length" greater than one. These examples have a much richer structure than conifolds. A picture is proposed that relates matrix factorizations in Landau-Ginzburg theories to the way that matrix factorizations are used in this paper to perform noncommutative resolutions.

33 pages, (minor changes)

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• Brane Tilings and Exceptional Collections
• The Geometry of D-Brane Superpotentials
• Decompactifications and Massless D-Branes in Hybrid Models
• Remarks on quiver gauge theories from open topological string theory

Cited by in corpus (14)

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• Geometric engineering on flops of length two
• Holography, Matrix Factorizations and K-stability
• Gopakumar-Vafa invariants do not determine flops
• Topological Strings on Non-Commutative Resolutions
• Rational Curves and (0,2)-Deformations
• Expanding on the Cardy-like limit of the superconformal index of 4d $\mathcal{N}=1$ ABCD SCFTs
• Attractor invariants, brane tilings and crystals
• Effective Superpotentials of Type II D-brane/F-theory on Compact Complete Intersection Calabi-Yau Threefolds
• On holographic duals of certain isolated weighted Gorenstein cDV singularities