Brane Tilings and Non-Commutative Geometry

Abstract

We derive the quiver gauge theory on the world-volume of D3-branes transverse to an L(a,b,c) singularity by computing the endomorphism algebra of a tilting object first constructed by Van den Bergh. The quiver gauge theory can be concisely specified by an embedding of a graph into a face-centered cubic lattice. In this description, planar Seiberg dualities of the gauge theory act by changing the graph embedding. We use this description of Seiberg duality to show these quiver gauge theories possess periodic Seiberg dualities whose existence was expected from the AdS/CFT correspondence.

23 pages; v2: reference added, minor changes

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Cited by in corpus (8)

• Colored BPS Pyramid Partition Functions, Quivers and Cluster Transformations
• Cellular resolutions of noncommutative toric algebras from superpotentials
• Instantons, Quivers and Noncommutative Donaldson-Thomas Theory
• Y-meshes and generalized pentagram maps
• Holomorphic field theories and Calabi--Yau algebras
• On Exactly Marginal Deformations Dual to $B$-Field Moduli of IIB Theory on SE${}_5$
• Cascades with Adjoint Matter: Adjoint Transitions
• New dimer integrable systems and defects in five dimensional gauge theory