Communications in Mathematical Physics

, Volume 313, Issue 3, pp 607–633 | Cite as

Quivers from Matrix Factorizations

Article

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 \({\mathbb{P}^1}\) 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.

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Center for Geometry and Theoretical PhysicsDuke UniversityDurhamUSA
  2. 2.Departments of Mathematics and PhysicsUniversity of CaliforniaSanta BarbaraUSA

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