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Dimer models and Calabi-Yau algebras

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arxiv 0901.4662 v2 pith:PUWMMMBQ submitted 2009-01-29 math.AG

Dimer models and Calabi-Yau algebras

classification math.AG
keywords dimeralgebrascalabi-yauconsistentmodelmodelsalgebraalgebraically
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In this article we study dimer models, as introduced in string theory, which give a way of writing down a class of non-commutative `superpotential' algebras. Some examples are 3-dimensional Calabi-Yau algebras, as defined by Ginzburg, and some are not. We consider two types of `consistency' condition on dimer models, and show that a `geometrically consistent' model is `algebraically consistent'. We prove that the algebra obtained from an algebraically consistent dimer model is a 3-dimensional Calabi-Yau algebra and finally prove that this gives a non-commutative crepant resolution of the Gorenstein affine toric threefold associated to the dimer model.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Quiver-Invariant Dualities between Brane Tilings

    hep-th 2026-01 conditional novelty 6.0

    A tilting mutation of brane tilings yields distinct superpotentials on the same quiver with identical mesonic moduli space, equivalent to a sequence of Seiberg dualities.

  2. Machine Learning Toric Duality in Brane Tilings

    hep-th 2024-09 unverdicted novelty 5.0

    Neural networks classify Seiberg dual classes on Z_m x Z_n orbifolds with R^2=0.988 and predict toric multiplicities for Y^{6,0} with mean absolute error 0.021 under fixed Kasteleyn representative.